There was the idea of the "Sea Control" ship in the 70s that would have built on this idea: https://en.wikipedia.org/wiki/Sea_Control_Ship

For small-scale conflicts however, it's somewhat paradoxical that a large carrier is what you need. Putting airpower over land from a carrier requires throwing a lot of weight into the air to put an aircraft with both an effective warload and a useful loiter time. This is coupled with a large sortie rate, as the time it takes to get a warplane on station is long and needs to be replaced often. That adds up to a lot of launches.

All of that is to say then that you need a larger carrier, ideally with a catapult and the powerplant to fire it often. Skijumps and STOVL don't get you that kind of range except to the beach.

So for any kind of land strike mission, you really need a big fleet carrier. But for sea operations, smaller carriers are looking more feasable, so the idea is coming around again. The America class as you mentioned is likely going down this path, and Japan's Izumo-class is likely going to go down this route as well.