I must honestly say that I'm not an expert in military matters, but I heard that China has pretty good conventional (non-nuclear) anti-ship missiles. Please correct me if I'm wrong/misinformed.
If these are really good, that could be a cheap modern way to kill carriers.
They represent a
possible threat. The US Navy has spent the last half-century developing and fielding ways to protect their Carriers from threats. Communist-made weapon systems have a strong history of being over-hyped by those who develop them, but not being anywhere near that impressive. Still dangerous, but nowhere near as capable as claimed.
All of that said, a mass-launch saturation attack would probably actually be fairly dangerous to a carrier group,
if they can send them all into the correct target area. Practically speaking, I expect that the Chinese
might be able to destroy a single Carrier, but in doing so they'd expend their ability to threaten a carrier group, both due to how many missiles they'd have to use, and counter-strikes taking out a fair bit of their arsenal.
Now, if the Chinese missiles
actually perform somewhere approaching the level Chinese PR says they will, then...
US Carriers will have to operate from further away in the event of a war. They'd sink one, maybe two if the pair in the SCS are still sailing together, but after that, the US Navy just wouldn't move them into a range where they can reasonably be threatened. It'd degrade response and loiter times for USN aircraft supporting Taiwan (or whatever less likely circumstance they need to act in), but it wouldn't destroy it altogether.
Unless the PLAN gets to the point where their own Carriers are a fully peer threat to an American Supercarrier task force, the Chinese still will not be able to challenge the USN on the high seas, which means that they can't force the US to stop supporting regional allies. Even if the Chinese do get to that point, we have five times as many Carriers as they do, and ours are bigger besides.