I think you got this turned around. Carrier operations is all about using the aircraft as offensive weapon. The fleet is there to protect the carrier which carries the offensive weapon. That is because the using aircraft as offensive weapon has advantages such as range, sustainability, better fire power and lower cost per bomb.But tbh, PLAN's CV should focus more on defending the fleet than working as a striking platform. China now has advanced hypersonic missiles, possibly they will put them on board, carried by giant destroyers, which seems to be a better anti-navy weapon than air2navy missiles carried by aircraft. On the other hand, PLAN needs to face attacks both from the US's CVs and bombers from their overseas airbases. Thus to effectively protect the fleet, what they need should be a bigger aircraft, instead of a smaller FC-31 size one. That's why I think the model we see here is still verifying aircraft, the same as the preceding FC-31 family. And don't forget, their current model is J-15, one of the biggest carrier fighters ever in the world.
The reason that the US turns to smaller F-35 and gives up NATF is definitely the collapse of USSR and sudden relief of air-defend stress to the CV. Also they quickly retire all the F-14 and AIM-54, and turn to multi-function FA18.
As to having bigger missiles and bigger aircraft, you have to think of the whole thing as a package. If you increase the size of the missile or aircraft, you increase the range for these weapons, but would the fleet be able to see that far out? A carrier group with AWACS circling on top can only see another ship 200-300 km out no matter the size of the radar. This will not increase even if you switch to next gen aircraft that has the range of 10,000 miles. The large missiles will likely mean a very large ship, but if you can't see what you are hitting, then it does you no good to blindly extend the range of the missile without also the ability to acquire your target further out. Unfortunately acquiring target further out is limited by the curvature of the earth.
The U.S. was thinking of attacking land based targets in China. To avoid the defensive missiles like the DF series, they need a longer range aircraft. Even there, as the Chinese can reach out further to touch someone, the increased range of the aircraft simply can't keep up with the advancement in missile technology. At the open sea fighting another carrier group that move about, larger missiles and planes don't make that much sense if you can't find the target.