I don't get why there's one Academy - surely that wouldn't provide enough graduates for one planet, let alone a union of hundreds of planets... Not unless the academy covers the whole of San Francisco, or something ridiculous like that.
Why would a citywide Academy be ridiculous?
Surely there's nothing impossible or impracticable about processing all the officer hopefuls (and possibly also the enlisteds) through San Francisco. The United States Navy today has some 330,000 personnel, and its primary institute of education processes 4,400 students per batch. If Starfleet maintained a similar ratio of one officer student per every 75 active servicemen, a force ten million creatures strong (say, some 10,000 ships with 500 crew apiece on the average, plus the same number of support personnel) would need to process some 135,000 students. Several universities today claim this sort of attendeeship, even if partially via remote studying. Logistically, cramming 135,000 people (or four times that many, assuming all these folks stay for four years) in a single city for unity-building ceremonies and joint courses wouldn't be a problem, either.
In a military as diverse as Starfleet appears to be, unity would be of essence. Having a single location for graduation would enforce that unity quite nicely. Not to mention that it would be an important pilgrimage to the capital world, the first one for many.
Tackling this from the other end, there's no onscreen evidence that people could graduate from other locations, even though people may attend the entry exams elsewhere, and probably can take courses outside San Francisco as well.
Timo Saloniemi