Why do you think the US Navy does not need 'lots of ASW convoy escorts'? The Chinese submarine fleet as well as the Russian are not small, and logistics are a significant issue (not only) in the Pacific.

ASW is not currently a strength of the USN. I think it lacks ASW ships to protect both the carriers and the convoys.

I am not sure if smaller ASW carriers would be the solution, although they were seen as such in the late stages of the Cold War, when a number of small European ASW carriers were introduced. At that time, USN supercarriers also had significant ASW forces on board, but these have long since disappeared.