China can almost certainly win a naval war with the US already; or rather, negate the US's naval force projection tool of choice, the aircraft carrier, with anti-ship ballistic missiles.
Every Carrier Battle Group has two ships in it that are essentially devoted to just protecting the carrier whether from missiles or other threats. We've yet to see how effective systems like Aegis are against anti-ship missiles (though I'm sure the DoD has done plenty of tests) but it's far from clear that anti-ship missiles obsolete carriers. And given that China is starting their own carrier fleets I'm guessing they don't think things are so clear cut either.
The Exocet was made way back in the early 70's yet carriers and surface fleets in general still aren't obsolete.
Of course a lot of this is self-serving stuff designed to drum up more money to spend, but defence against missiles is fundamentally asymmetric. The defender need to get lucky every time, while the attacker only needs to be lucky once or twice. And MIRV is a big multiplier in favour of the attacker.
Carriers are great against countries or factions without anti-ship missile capability.
Can those ballistic missiles actually hit anything?
They're converted ICBMs, and require some kind of terminal guidance. Something traveling Mach 10+ can't use radar or infrared guidance. How does it hit a maneuvering ship?
Current thinking is drones or some other local surveillance would be used, radio linked to the DF-21. I wonder how well that will work alongside US electronic warfare capabilities?
those are ballistic missiles, can they even hit a moving target? Besides, if it comes to it, after sinking an aircraft carrier the US Congress would have no choice but a full declaration of war. That means SLBMs engaged (ie Tridents) before surrender, it would be the end of the world.
https://en.wikipedia.org/wiki/DF-26 - range of 2500 miles