The problem is that to saturate the defences of a carrier's escorts you need hundreds of missiles not dozens. The Chinese have lots of missiles but not an infinite amount; especially not of the modern, purpose-built weapons that can pose a real threat to the carriers.

In reality they're going to have just a few tries before they run out of ammo. Just shooting at everything that might be a carrier is a great way to lose the war.

To actually pull this off you need to be able to rapidly locate and identify the target, communicate it's location to all your various launchers, then coordinate a complex time-on-target attack between all of them.

Any mistakes or disruptions in the chain can ruin your whole attack; misidentify the target and your attack misses, fail to communicate and a portion of your launchers never fire, fail to coordinate and your missiles arrive too spread out and are shot down, take too long to do all of this and the carrier will clear datum and you're stuck waiting for the next pass of a recon satellite that may never come.

This is all extremely difficult even under ideal conditions let alone when Uncle Sam is jamming your comms and blowing up your servers.

Not to say it's impossible, just that it's not as easy as you may think and that accurate targeting is a major factor.