Which still wouldn't address the time needed to travel there, even IF you could them all in one planet and one facility.
That's exactly what it
would do, as travel time by transporter is essentially zero. Of course, virtual presence would take care of much of it anyway, as it allows for universities with hundreds of thousands of students today already.
You can't transport from planet to planet, from star to star. With the size of the Federation it could take months, even YEARS, before they finally find themselves on Earth. They'de be transiting longer to get to academy in some extreme cases, than they'd attend the academy.
As for traveling from one's homeworld to San Francisco, there's no support for the idea that any known part of the Federation would lie beyond a travel time of several years from Earth. Somehow, the distances and warp speeds work together to create a Federation accessible by starship within the context of the plot. And what if travel there takes six months? It's just part of the great unifying experience.
8,000 lightyears, that means at Warp 9 it takes 8 YEARS to get to Earth at the most pessimistic, 3 YEARS at the most optimistic. It would make them traveling longer than they'd be at the Academy. And 6 months, aka a year of travel time back and forth. (Oh, do remember, I lied in the above example, I'm actually being EXTREMELY optimistic with even the most pessimistic number - this is after all the number, of several years of sustained Warp 9 flight.)
With the amount of students there are, you'd need more ships just to shuttle the graduated ensigns to their new assignments than actually doing any work.
It is just not feasible.
Perhaps there are outlying holdings 8,000 ly from Earth that cannot effectively participate in Starfleet training because the cadets would need to travel for three-four years to reach the Earth facility. But such holdings wouldn't benefit much from a local training center, either, when Starfleet itself lies closer to the core worlds and cannot respond quickly to a threat against such an "island".
They would have their own training center, they'd have to man their own defense force. Whether it gets the name Starfleet is another question, and I would at a guess say, yes:
Which is exactly the point. What is a satellite in past, is one of the "core worlds" or "main body" now. Yet the distance to Earth is still as great, and there's barely been a speed increase - only with with Intrepid-class do we have indefinite high-warp sustainable engines. It would take massive amounts of time to get to Earth back when they were satellites, and still today. The satellites self-setup, would become the Starfleet Academy for the region.
The thing is, you can jump high and low, but you'll never convince me that "Earth is the only place with a Starfleet Academy" is not a ridiculous concept. We should have heard of Starfleet Academies on other worlds by now, that's my opinion and I'm sticking to it.
The foreign navies would have the same numbers. And we've never seen many figures quoted if at all, most certainly not figures that encompass the entire Starfleet.
I know you are very fond of selective acceptance of evidence - all of us are, around here, to greater or lesser degree. But these figures most definitely are there: DS9 speaks of Starfleet formations called "Fleets" involving hundreds of ships, in a way that precludes them from involving thousands, and mentions several of them, but never a Fleet numbered higher than 10. It's statistically utterly implausible, then, that there would exist sixty Fleets, or that all the unseen ones would be larger than the witnessed ones.
Before DS9, we had little or no data to judge Starfleet's size by. After DS9, we have it more or less nailed down for us.
Not so much, because we've only heard numbers after battles and after a major war, where they've always said they've lost lots of ships.
Also, fleets only exist in war time, during peace the ships are much more spread out. I would hazzard a guess, that not all ships are assigned to war fleets.
60 fleets of some several hundred ships, I find horrendously little for the size of the Federation.
The "only the Enterprise is in range" said I mostly ignore as anything but flukes, required to get the story going. Taking that as reality would make no sense.
I know you have problems accepting any reality but your own. But this
is Star Trek we are talking about. Your alternate scifi show should really get a forum of its own.

Anyone who takes plot-contrivances as a way to measure numbers is ridiculous.
The Enterprise-B is the most horrendous violation of this. How in hell, can the capital of the Federation, the solar system with one of the main fleet yards, a system that should attract MASSIVE amounts of traffic, both Starfleet and civilian, and is the system that by default should have one of the most heavy defensive presence and patrols even without all the traffic flying around, have but one, incomplete starship around?
This so completely makes no sense whatsoever, to take that as a sign for Starfleet's numbers is ridiculous.
If only half those members have the amount of colonies that the Humans and Vulcans have, we'll already be in the 5 digits, and it's probably more.
The amount of colonies Earth has is unknown, but onscreen count hardly goes past fifty. And you don't know of any Vulcan settlements of worth (because you don't accept ENT). So what to make of the "We're on a thousand planets and spreading" line of Kirk's? Doesn't sound applicable to the human species in light of this, but does sound plausible for a Federation where a percentage of 150 species push into space.[/quote]
Uh, there aren't a 150 species until the latter half of the 24th century. There were a lot less by TOS. And for the size of the Federation, a thousand planets with humans (many amongst them mixed with other species no doubt) sounds quite right actually. The total number of worlds under the UFP in the TOS area I would hazzard a guess by that number is close to 10,000, which by the 24th century would be double that or more.
Also, the number of colonies attributed to individual members, rather than to the Federation, is pretty much zip anyway. That is, after the founding of the UFP, but material from ENT supposedly doesn't count.

Absence of evidence, is not evidence of absence.
However, you'd be wrong. We've seen quite a few a colonies set up that are quite new, which means that even in the 24th century new colonies are being established all the time. Not among the least of which, the colonies that would later become the Cardassian-Federation DMZ.
So we know the spreading didn't stop.