Had a great use of aircraft carriers in my 500 turn score victory game. Obviously carriers aren't particularly useful if you are going to get a culture win at or before turn 250. I urge everyone to try one 500 turn score victory game (disable all other victories). Obviously you are going to want to engage in late wars, don't friend everybody! That would be extremely boring pressing end turn all the time. It's worth it to see some late unit action.
GDR's by themselves really aren't all that. No matter how strong they are, they only get 1 attack per turn. This is where carriers, and jet bombers shine. Obviously this is more useful on continents or water maps. In my particular case it was a continents huge map. My mission? Just liberate city states in the late game. I only had enough uranium for 1 GDR. So I really needed support units. And carriers fill this role. I have found attacking cities with jet bombers foolish as they are instantly shot down by jet fighters. But jet bombers are quite effective for eliminating enemy troops in the field. I thought jet fighter deploy mission covered a certain area, but either I'm mistaken or the AI doesn't get this. As I said, GDR only gets 1 attack per round, use those carriers and jet bombers to obliterate enemy armies out in the field. I wouldn't have been able to accomplish my mission of liberating city states without carriers. I liberated all the city states from China and India (Chandragupta) by the end of the game. They had reconquered a couple, and I liberated them again. Thankfully neither one had enough uranium to field GDR's (the AI stupidly builds nuclear power plants and lets them melt down), though I could have handled 1 with no problem. I admit, had I faced Russia and their 15 GDR's, I would have been hurting, but Russia was my military ally. So choose your wars wisely. But keep in mind jet bombers are effective against GDR's. I know because my GDR was taken to about 25% health from one attack from a jet bomber.