I would remind you that the Yamato heavily outclassed the aircraft carriers that sank it in both weaponry and armor, but it came up short in range.
If you are meeting an enemy in a flat barren desert, would you rather have a .30 carbine or a stub nose .44 mag revolver? I’d take the rifle all week long and twice on Sunday.
The Sovremenny DDGs can’t survive a USN airstrike, and they will be within range of airstrikes for well over 10 hours before they close within SS-N-22 range. As I said, anyone can conduct a surprise attack once, just as anyone can be murdered if the attacker acts without motive or warning, but it gets much harder after that first round.
The Moskit, and it’s newer Onyx/Yakhont variant, are modified to be lauched from submarines as well as from the Su-27 (which the Chinese have) and the Su-33 (which the J-15 is based upon). Moreover, the SS-N-26 has a range of close to 200 miles.
With the assets available from the Chinese mainland, the PLA/PLAN are easily able to launch saturation attacks on a carrier battle group. This holds especially true if the CVN and its attendant screen enter the Taiwan Strait. Purely from the perspective of numerical advantage, a carrier battle group would not survive 50-100 incoming ASMs moving at Mach 2, especially considering some (or all) of them will be armed with nuclear warheads.