Effectively, they're 1950s versions of the 1970s Sea Control Ship idea, i.e. a secondary, deck-multiplying asset for the USN but a primary for somewhere like Spain or Italy.
The problem with replacing ships with aircraft, certainly in the 1950s and until very recently, is that the latter are fine as long as they're working, flying, in the right place and still in one piece.
1. Aircraft go unservicable, the more so the longer they keep flying high intensity ops, and even the best carriers have limited abilities to repair them. Warships are relatively more reliable and durable, so the escort's guns, missiles and depth charges will still be working long after most of the aircraft have become hangar queens.
2. Until relatively recently, air ops could be shut down completely by weather conditions, and even if they were flying, their effectiveness was severely reduced by night or bad weather. The AAW escort is still ten miles up-threat, even in the worst weather.
3. Once airborne, aircraft are no longer "tied" to the carrier, and can be decoyed, mislead or chased away. The weapons on the escort ships will always be there because they can't go anywhere else.
4. Aircraft crash and get shot down. It's not unknown for carriers to be forced to withdrawn from combat simply because they don't have a viable force left. Again, on the day after you've reached this point, you still need to defend your force, which you can only do with the escorts because they're all that's left.
All of these factors are much more significant the smaller the carrier is, because each individual aircraft represents a greater percentage of the ships totla air group. For instance, if two USN Hornets collided and crashed in bad weather it'd be tragic, but it would only reduce the super-carrier's offensive/defensive air power by just over 4% (assuming she has 48 x Hornets). By contrast, when two of HMS Hermes' SHARs collided and crashed in bad weather during the Falklands war, it reduced the carrier's air power by nearly 17% purely because she only had 12 to begin with.
You idea isn't a bad one, it just needs to recognise the neccessity for escort ships. If you look at small carriers task groups fielded by any nation, they almost inevitably consist of the carrier, two or three escorts, and a supply ship. By the way, the latter is not merely a logistics asset, at least in the RN. The latter's biggest replen ships can operate up the FIVE Merlins, and provide greater maintenance support for them than the frigates, so putting say, a Fort Victoria in a force with Type 23 frigates actually increased the combat effectiveness/persistance of the latter.