There's also the fact that in order to support a Starfleet the size of which we've seen, they need more than one "academy" to create that many officers. Yet we only ever hear of the academy in San Francisco. There are a few smaller schools, but they seem to be annexes rather than separate schools.
It doesn't have to be as long as Starfleet has some kind of OCS program. But, and I've brought this up several times in the past, there's never been any indication that it does.
Bones is a good example. He went to Ol' Miss and then went on to medical school. If he were to join the modern navy, all he'd have to do is enroll in OCS. But instead he went to the Academy.
I can understand where a Starfleet training program would have to be slightly more involved than just the basic military training of today's programs, but you'd have to think that a 24C degree in astrophysics from MIT or CalTech is just as good as the one you'd get from the Academy. No reason to go back and learn all that over again.