>When was the last serious naval battle?
Probably WWII. But that's not a good metric: the purpose of the modern American Navy is to project force, and also to act as a deterrent. When the US can sit a carrier battle group a few dozen miles off the shore of your country, carrying a rather enormous amount of firepower and the ability to deliver it anywhere within 1000km of that, not many are going to want to challenge that.
>When an aircraft carrier can project force out thousands of km you really don't need a lot of them.
F/A-18s can't fly that far. I just looked up the Super Hornet on Wikipedia and it says the combat radius is just over 700km. (The straight-line range is 2346km, but that's not helpful if you want to get back to the ship and doesn't include actual combat maneuvers and a decent reserve.)
So if you want to be able to project force in multiple areas of the world, you'll need that many carrier groups. It's not like a carrier in the Persian Gulf can fly some planes over to India if they need to. Also, Navy ships (just like military aircraft) need a LOT of maintenance, so there's always a bunch of ships in port.
We don't have the technology to have solar-powered drones that can carry ordnance.