Two is not enough
Definitely the Navy should be in charge of its air capabilities but surely two big ones are never going to be in the right plce at the right time and you would be lucky if even one is ready at short notice. On top of that you need a great deal of resources to protect them , destroyers , air defense, submarines , half the current Navy would be committed just to look after the carriers. And with anti ship missiles getting faster and cheaper every year the problem is only going to get worse.
Big things just make big targets , it would be much better to go for smaller cheaper smarter solutions