We haven’t had a real naval battle in 40 years, arguably 80. Since that time, sensors of all types have become vastly more numerous and capable, as have missiles. I don’t see how a surface ship survives in that environment.
In a shooting war between the US and China, the US will try to establish air and sea dominance. That means in the first days or weeks of the war, it would keep away its vulnerable assets, such as non-stealth aircraft, or surface vessels that are not part of carrier strike groups. It would make use of stealth fighters and bombers, cruise missiles, and in the sea domain, submarines and carrier strike groups.
After dominance is established, all the other assets become very valuable.
If your enemy has access to satellites, long range sensors, submarines that can fire hypersonic anti-ship missiles, and modern air defense systems, then a strategy based on the assumption of air dominance will fail.
Let's also not forget that the U.S. has never achieved air dominance over any nation with sophisticated air defense systems. The last time the U.S. actually tried to fight an air war against an enemy with access to relatively modern air-defense systems was in Vietnam, where 3700 US planes were shot down (and about 5000 helicopters). Air defenses are much better now, which is why Israel - with its advanced F35s -- is so afraid of Syria's S300 systems that it only uses standoff weapons when it raids Syria, proving once again that long range missiles are what matters, and outdated concepts like "air dominance" are only relevant when the enemy is limited to RPGs and Toyota trucks.
When the US has air dominance, the only strategy to launch missiles - of any type - is shoot-and-scoot. That can work with man portable missiles like Javelin, or pickup-truck mounted missiles. But it won't work with anti ship missiles. Those you can launch from large platforms, such as huge trucks, surface vessels, ground silos, or aircraft. If the US has air dominance, all of these are as good as dead once they fire their missiles.
Hypersonic carrier-killer missiles won't work for the same reason Russian SAMs are minimally effective against western air forces: if you know where the launcher is, you tread carefully until it is destroyed. The United States has possessed the MASINT/ELINT capability to detect the location and type of practically every RF emitter in a given area from space since at least the mid-1980s.
Assuming, of course, any nation that develops hypersonic carrier cruise missiles can figure out how to steer them at a hypersonic velocity in thick air. Something extremely smart people who would make an extremely large amount of money if it was possible have told me is extremely impossible.
Land-based anti-shipping missiles won’t be in short supply in any such conflict.