I believe the "small navy" was a political and technological requirement and not something you'd need today. A single ship ought to do now.
Political, because it was the Space Race, and a lot of it was about shows of force. And hey, why not? You have a bunch of carrier battle groups just waiting around for a hot war, and you need to have them out training anyway, so why not use them to pick up spacecraft from time to time?
Technological, because guidance wasn't necessarily very accurate. It's interesting to look at the miss distances here:
Some of these landed hundreds of miles from their target. However, by the time Apollo came around, they were all very close. You definitely want a big recovery fleet to cover a lot of area when you can't be sure it'll land on target, but that's not so much of an issue these days.
I remember reading about the issue in a book called "This New Ocean"
apparently by the time Apollo was on the go NASA had to ask the military to position the ships off to the side of the splashdown zone - the guidance improved so dramatically they were afraid of hitting the carrier directly
