Current Paradigm of Warfare's Future
Smart weapons that go faster and further.
Precision Guided Munitions
More capable computer chips and software have led to an explosion in the capability of guided munitions. These weapons are an order of magnitude more effective than their unguided predecessors.
The range of weapons is constantly increasing. If an anti-ship missile with a 200-mile range is good, one with a 2000-mile range is better.
Speed and maneuverability are paramount. Air defense missiles also improved, leading to a cat and mouse game. Missiles will often do wild maneuvers right before impact to deter countermeasures.
Peak weapon is hypersonic cruise missiles that can fly at low altitudes and outmaneuver any threat. 
If you are traveling at Mach 5, you better know where you are going. Drones and satellites have seen rapid improvements that allow them to find the enemy and direct guided weapons.
Long-range missiles like China's DF-26 "Aircraft Carrier Killer" would be significantly less effective without targeting information from satellites, submarines, or long-range drones.
Anti-Access and Area Denial
The primary change in strategy driven by better missiles is known as anti-access and area denial (A2/AD). China has aggressively adopted this strategy after seeing the US military dominate Iraqi forces in 1991 and being embarrassed by the US sending carrier strike groups through the Taiwan Strait.
Their doctrine has been to buy enough missiles to overwhelm US ships and make operating near China impossible. These missiles are also capable of striking regional US bases and rendering them unusable. Many analysts think China could succeed in clearing the US Navy out of the First Island Chain (Taiwan, Japan, Philippines), and some think missiles like the DF-26 could push that out to the Second Island Chain (Guam).
The overarching goal is to prevent the US from projecting power near China and prevent the US from intervening in the case of a Chinese attack on Taiwan or a Chinese expansion in the South China Sea.
As a response, The US is building longer-range missiles, building a new series of stealth bombers, adding new frigates, improving missile defense, and developing cheaper unmanned planes and submarines. Many analysts feel these efforts may not be enough to deter China as it continues to grow military spending and develops new weapons like hypersonic missiles.
SpaceX's Starship is a classic dual-use technology.
What is Starship?
SpaceX's long-term vision is to create technologies that allow Mars colonization. At the top of the "need" list is a dramatic reduction in launch cost to orbit. The Starship launch system fulfills that goal in several ways:
It is fully reusable.
All previous rockets expend expensive pieces of hardware.
It has an extreme flight rate.
The plan is for each booster to launch every few hours. Flight rate is key for fixed cost absorption.
The rocket itself is cheap.
Made of materials like stainless steel, Starship would be one of the most cost-effective rockets even if it wasn't reusable.
It uses cheap fuel.
Methane and oxygen are very affordable and available fuels.
The goal is for the marginal cost of launch to be as low as $10/kg. That is a low cost compared to the previous launch vehicles - over two orders of magnitude in improvement. What to do with cheap launch becomes an ongoing question.
There is a decent probability that Starship's first orbital flight will happen in 2022.
Space-Based Kinetic Weapons
Rods from God
Objects falling from orbit carry incredible levels of kinetic energy. Weapons utilizing this principle are popular in sci-fi, famously appearing in "The Moon is Harsh Mistress" and "The Expanse."
In the 1950s, a Boeing engineer envisioned dropping telephone pole-sized tungsten rods onto targets from orbit. The impact would be equivalent to over ten tons of TNT, and the rod could penetrate hundreds of feet underground to destroy bunkers.
The US has considered developing this weapon several times but elected not to because nuclear-tipped ICBMs or conventional bombs were more capable at a lower cost. Each tungsten rod would weigh almost ten tons and cost a fortune to loft into orbit.
Rethinking Kinetic Weapons
Since orbital launch costs were high, only a few rods would be in orbit. Tungsten was a natural choice because its high melting point allows it to survive reentry and its high density maximizes kinetic energy.
The crazy low cost of Starship changes the logic. B-52s flying from Barksdale AFB to complete a mission in East Asia incur a marginal cost of $50/kg to deliver bombs. Starships cost is cheaper and can put weapons on target in less than thirty minutes. Each Starship launch has the same payload as three B-52s. The world only produces around 70,000 tons of tungsten per year, and 90% of that comes from China. That is only enough for 700 Starship bombing runs, plus tungsten costs around $30/kg.
Another option is kinetic weapons made of iron, stainless steel, or depleted uranium. Iron and stainless steel are cheap, available, and have high enough melting points to survive reentry under proper design choices. Launching dumb iron rods from the continental US would have a similar cost per explosive power as a standard artillery shell. Depleted uranium has a similar density as tungsten. Protective casings could allow the delivery of ordnance like GPS-guided JDAM bombs. The supply line would be a natural gas pipeline and a rail line providing fuel and projectiles to a domestic launchpad instead of ships crossing oceans.
Possible Design Configurations
Mass and velocity determine the energy a kinetic projectile has.
energy = mass * velocity^2
Most projectiles reach terminal velocity when falling through our thick atmosphere. Mass and drag determine terminal velocity. Objects made of denser material in aerodynamic shapes have much higher terminal velocities. The tradeoff is that they are also exposed to much higher temperatures as they scream through the atmosphere. You could design a long, aerodynamic steel rod that would reach incredible speed but vaporize in the air. Tungsten has both the highest density and highest melting point of any metal, making it the energy on target king.
Other projectile types can struggle because the drag needed to shed velocity in the thin atmosphere to lower peak heating significantly slows down their terminal velocity in the lower atmosphere. The energy is still significant. 20-gram "Lazy Dog" projectiles launched from aircraft pack as much punch as a bullet. But that isn't enough to pierce armor.
Lazy Dog Projectiles, Source: Global Security
Many tanks use sabot rounds. These are kinetic weapons that have a dense rod inside a protective casing. The casing stabilizes the skinny rod in the tank barrel and ejects it once in flight. A similar concept could allow rods made of depleted uranium, iron, or steel to make it through the atmosphere and still have shapes with high terminal velocity. The casing could carry a wide range of projectile sizes and quantities.
A Sabot Round, Source: Wikipedia
Unguided ballistic projectiles can hit a target within a few hundred meters. That level of accuracy is adequate for a Mach 10 tungsten rod because of its energy. It works for rounds with large amounts of smaller projectiles and shotgun-style spreads. Today's armies regularly use Multiple Launch Rocket Systems with similar qualities.
Sabot-style rounds can use GPS to steer. When rods leave the sabot, they will only be seconds away from the target, and accuracy will improve. It is also possible to build shells that allow the delivery of traditional smart weapons like JDAMs or Small Diameter Bombs.
Utilizing StarLink's Sensing Capabilities
Orbital weapons still need intelligence to tell them where to go. Starship's sister system, StarLink, provides an answer. StarLink is a constellation of thousands of small Low Earth Orbit satellites that gives customers low latency broadband internet. It uses sophisticated phased-array radios that allow ground terminals to track satellites traveling thousands of miles per hour.
As Casey Handmer points out, StarLink can use its radios to do high fidelity synthetic aperture radar (SAR). SAR is already one of the primary ways militaries find enemy ships, and researchers have used it to track planes. It could also see ground vehicles.
While the US already has satellites capable of doing this, they are expensive and limited in number. Individual StarLink satellites cost a few hundred thousand apiece to build and launch on Starship. One of the first things China would do in war is shoot down our military satellites with anti-satellite missiles. That is a problem with bespoke satellites but not with Starlink. Anti-Satellite missiles cost tens of millions of dollars. Each Starship launch could drop off hundred of StarLink satellites. The Chinese would have to expend incredible resources to keep StarLink offline.
A satellite constellation provides other bonuses. Our GPS satellites are both hard to replace and sensitive to jamming. StarLink can provide GPS coordinates (with a few meters less accuracy), and its phased array radios make it difficult to jam.
The upshot is StarLink gives the US survivable sensing, communication, and navigation capabilities.
Instead of the US military using expensive missiles for satellite shootdowns and risk increasing orbital debris, Starship can capture enemy satellites, Blofeld-style, or release smaller, cheaper kinetic weapons.
Starship is also cheap enough to clean debris if they threaten US satellites.
Imagining a Doctrine
Basic Stike Modes
The first mode is lobbing projectiles on a suborbital trajectory. A strike like this would take 30-60 minutes to reach a target and is the simplest method. The elapsed time and rocket readiness would be an issue for targets of opportunity.
The second is dropping off weapons to "loiter" in Low Earth Orbit until needed. The projectiles would be attached to a thruster that could deorbit and release them to send them on their way to a target. Pre-positioned weapons are more complex, but you could space them where time on target is only a few minutes anywhere in the world. The cost of this type of technology has been plummeting.
Controlling the Seas
Modern anti-ship missiles are cheap compared to the ships they attack, but they are still pricey. A medium-range missile costs millions, and a longer-range one costs tens of millions. Enemy ships would shoot down the vast majority of missiles during an attack. In comparison, iron costs $0.10/kg. The GPS guidance kit for the JDAM bomb costs ~$20,000. A sabot cover could be affordable compared to other space hardware because it only has to do one thing and Starship makes mass less of a concern. A single Starship could dump off the explosive equivalent of 100 missiles for less money than one long-range missile.
Hitting moving ships is still no easy feat. Ships can cover a lot of distance even within the few minutes it takes to deorbit. Launching unguided weapons would require a lot of mass to get a few hits. Current US weapons either use radar for terminal guidance or follow lasers. GPS bombs haven't been able to change attack coordinates in flight until recently. The Air Force's "Golden Horde" program is testing that ability. The ideal first strike might consist of GPS-guided sabot canisters fed attack coordinates from the StarLink constellation. They would dispense a shotgun pattern of smaller iron or depleted uranium penetrator rods above the enemy air-defense missile ceiling. A ship would only be able to travel ~1000 feet in those last seconds. The rods should achieve a "mission kill." Further strikes with heavier rods or bombs could follow.
There is already some debate that massed missile attacks can overwhelm ship defenses. Attacking ships with even larger quantities of kinetic weapons leaves them vulnerable. The only existing counter would be shooting at $100,000 sabot rounds with $10 million hit-to-kill anti-satellite missiles.
Clearing the Skies
The military could load a sleeker sabot round with pieces of shrapnel and again use StarLink to identify enemy planes. The rounds could bear down and release a cloud of shrapnel in the vicinity of the aircraft. Like anti-ship missiles, these projectiles would be a fraction of the cost with much more capability than existing missiles.
One capability the US desperately desires is the ability to hit ballistic missiles in their boost phase before they pick up speed. Launching projectiles from space can do it - just like the Star Wars Program envisioned.
These scenarios would require weapons to be pre-positioned in orbit to reduce time on target.
Weapons like JDAM and the Small Diameter Bomb are already inexpensive and good at what they do. The presence of civilians makes the cost of inaccuracy much higher. It would make sense to deliver these existing weapons on the new platform in most cases.
There are a few exceptions. Tungsten rods still have a comparative advantage in attacking bunkers or cratering runways. Using "Lazy Dog" projectiles like MLRS strikes would also be advantageous.
The immediate effect would be erasing doubt about the US's ability to project power in places like the First Island Chain. We could credibly say that no Chinese invasion fleet can make it across the Taiwan Strait. I doubt that one could make it across now if we fought with Taiwan, but the uncertainty China's strategy creates increases the risk of war.
Our defense against rogue states like North Korea would be much more robust. North Korea's ability to hit anywhere in the US with nuclear ICBMs, with our only defense being later-stage interceptors, is an uncomfortable place to be. That type of ICBM technology is likely to spread to more countries.
Starship's capabilities provide the US with the next "offset" of military advantage.
Predicting the Fallout
New Weapons create reactions.
Weapon -> Counter Measure
Weapons are an endless cycle of new developments that opponents attempt to counter.
A few things immediately come to mind:
Like the nuclear race, the first order of business would be to build a Starship competitor. The Chinese are trying to construct reusable rockets in the Falcon 9 class but have not yet succeeded.
Increasing basic air-defense missile ceilings while making ships faster could at least force the attacker to overwhelm the defenses with bombs.
Another option might be building a laser similar to what Breakthrough Starshot envisions to send a probe to Alpha Centauri. It could shoot down any StarLink satellites that cross over it.
A desperate measure would be to dump space junk in StarLink's orbit. StarLink satellites are capable of maneuvering around debris. They can also fly at lower orbits where orbital decay is faster. The satellites themselves would have shorter lifetimes. Starship can also help clear the most dangerous junk faster.
Starship upper stages are more expensive than satellites or kinetic weapons. They would be priority targets.
Weapons and tactics that avoid orbital weapons will be more popular. Submarines, small drones, and concealed ground troops are systems less affected by kinetic weapons.
Weapons carried on Starship could quickly adjust to many of these countermeasures, starting the cycle anew.
Starship Extends the A2/AD Doctrine
If you threw 747s away after one flight, airline tickets would be prohibitively expensive. The same is true for throwing away hypersonic missiles after one flight. It is the wrong paradigm. Starship launching kinetic weapons is like having many more extremely capable missiles.
Since missiles are driving the anti-access area denial trend, Starship extends that. Kinetic weapons can do a lot of damage, but they can't capture cities or search a freighter. You could bombard cities, but nuclear weapons are still much more effective. China would still have short-range anti-ship missiles that keep US Navy ships from getting too close to its coast.
The United States has to control the ocean to defend our homeland - Mayhan is still relevant. Since Mayhan's day, technology has changed. You must dominate the air to control the sea. Now it means owning space, too.
Dual-use technologies always turn into weapons. If we don't do it, someone else will. I know I don't want to live in a world where a country like China controls the oceans. And simple kinetic weapons are just the start of what Starship can enable.
I don't quite understand the full "hypersonic" missile taxonomy. Ballistic missiles are often hypersonic and can have Multiple Independently Targetable Reentry Vehicles (MIRVs) that maneuver and avoid defenses. That is old technology. I think most people are referring to to hypersonic cruise missiles that fly at multiple mach speeds at low altitude. Most ballistic missile interceptors target the incoming missiles hundreds or thousands of miles away and often outside the atmosphere. It'd be harder to detect and engage a hypersonic cruise missile because of the curvature of the Earth. Some of these weapons could also be hybrids where they launch ballistically but reenter the atmosphere early to develop a cruise missile like flight pattern for the final attack sequence. Does it have to be Mach 5 at impact to be hypersonic? Or is being Mach 5 for only part of the way adequate? I'm sure there will be a full taxonomy at some point, if there isn't already.
The classic Elon Musk quote about Starship's design choices.