What is the right balance of Aircraft Carriers and Amphibious Assault ships?

LCDR (Join to see)
We could have all the carriers and amphibs in the world, but where will we get the Sailors to man them?

Oh, I know! Pull this old Squid (me) out of moth balls! :)

I'd start with a baseline of 13 carriers, and seriously consider ramping up to 15 by 2025, and 20 by 2035. This is a pretty modest plus-up (6 in the coming decade, tapering down to 5 in the next). Basically, we need to build enough carriers to replace hulls that will be hitting retirement in the coming decade PLUS enough to meet the 15-hull target, and then go to 1 carrier every other year. Build them for a 40-year service life, that means every other year we authorize and lay down another carrier.

Why so many? Because I really think that modern land-based TACAIR (operating from fixed land bases in-theater) is as dead as the leisure suit; that is an inevitable consequence of cheap PGMs. One large aircraft loaded with 160 SDBs can hit every aimpoint worth hitting on an airbase. Think on that a moment. What used to require a nuclear weapon to achieve (total destruction of military capability at a major airbase) can now be done with 40 tons of PGMs.

We're going to need TACAIR in theater, but the bases are going to have to be mobile--i.e., "carrier-based TACAIR" will be from the Department of Redundancy Department.

Land-based air is going to be strategic bombers, based in CONUS, and under a VERY robust aerospace defensive shield.

The problem with this question is this: at what point do you stop calling it an amphib and start calling it a carrier. An amphibious assault ship implies that the ship can be close enough to the shore to unleash the Marines without them being sitting ducks in the water for an extended period of time. Bigger ships are going to have a deeper draft. Deeper draft means staying further from the shore. Further from the shore means those Marines are a target for a longer period of time.
That being said, I think that there should be a two to one ratio of amphibs to carriers. If I was the leader of a nation, I would not want the United States to park a carrier, and two amphibs off my coast. That would be magnified by the carrier battle group. That would be the only thing worse would be seeing an entire carrier battle group parked off the coast.
I think that having two amphibs that can (as stated above) move close to the coast and discharge Marines almost on top of the beach head while aircraft from the carrier and two amphibs provide close air support would be a better idea than having an over abundance of air power with fewer boots on the ground. That is really the key. It is not really about Amphibious Assault Ships versus Carriers, it is really how much air power can we project while still having an effective efficient fighting force on the ground.
In a perfect world, you would have an equal number of each with the Carrier Air Wings "softening up" the landing site and then transitioning to Close Air Support while the Amphibs deploy the marines, provide Cobra Air Support and MEDEVAC of the wounded. How would you feel if you were the opposition force? You have your forces dug in, just waiting for juicy Marines to show up so you can kill Americans. Then it all turns to shit when Hornets and lightning and cobras oh my start dumping ordinance on your positions like you insulted their mothers. Then there is a break in the bombardment. You peak your head up only to find out that the beach head is infested with U.S. Marines. As you start get ready to fire and wipe out some Marines, those damned gunship pop up again. Now you have to keep your head down or have it removed. All because two carriers and two amphibs working in harmony just delivered a giant pain in the ass to your door step.
We don't live in a perfect world so tactics need to replace numbers. Fortunately we have the best trained fighter pilots in the world. So rule one establish Air Superiority this is done using the USAF and the USN. Rule two establish a landing zone. This is where the Navy and Marines step it up. This is where the two amphibious assault ships to one carrier comes in to play. Strike aircraft from the carrier soften it up, Marines land on the beach. Once you have that established, you start moving inland where you meet up with the Army guys who drove in from a neighboring country, or were dropped in behind the enemy. But that is another story for another posting.

So after blowing it up, My final answer is in a perfect world a one to one ratio would be best. In the real world two Amphibious Assault Ships for every one carrier.