If "they" can close MPA and successfully invade so could we. No-one is suggesting (I hope) that a carrier presence is how to defend FI. However, the deterrent effect of a carrier to such an adventure is that eventually we could come south, do as we did last time and close MPA (initially TLAMed, but subsequently cratered). With a decent carrier we'd be in a much better position than last time and CVS still offers ASaC (in the immediate future).
Without that option, it's game over boys. You can't get UNSC to back sanctions against I'm A Dinnerjacket and his bucket of sunshine band, so getting them to tell Johnny Gaucho to play nice is probably a non-starter too.
And yes, the FI is far from the only use of carrier air. The skill fade / loss argument is a far more compelling case, as is the answer to the question "Right X,Y,Z squadron RAF, please prepare for a two month deployment aboard HMS QE in support of JTFEX 15-01 please...."