In real life the U.S. island hopped in order to seize airfields to provide land based air cover for their fleet and also to provide land based air support for some of their invasions.
in Europe the allies also made sure their invasions were within range of land based air cover. North Africa possibly being an exception, though I do believe some land based air was provided from Gibraltar.
If ingame you can pull off invasions with just carrier air support, perhaps carrier air, in both ground attacks and air vs air, is to strong compared to land based air.
As far as Italy goes. I don't think the Italians should be to tough to make surrender. In real life they quit soon as they were invaded. After Italy's surrender, neither the Italian fascists or the Italian troops that joined the allies, were worth very much to their respective sides. Perhaps reducing the ground attack strength of carriers can solve the problem of defending Rome as well, without the need of giving Italy a 2nd capital.
Just my 2 cents. I'm about as far from an expert on this game as you can possibly get.