I tend to think we were only seeing the "Home Fleet" attacking Earth and Sol Station (or the Third Fleet that's said to be defending Earth in Deep Space Nine) . However, one thing to keep in mind is that the fleet numbers in the hundreds being thrown around in comments from Deep Space Nine was when the Federation was in a war footing. Presumably, there was a build-up during the run up to the Dominion War.This.
The fleet at Earth would have (in-universe at least) been a fairly small one... something you might expect to see closest to any UFP member planet at any given time.
In short, it was arelatively small contingent of vessels that was able to attend Frontier Day.
Otherwise, it makes no sense this was the whole SF from the entire Federation because they have diplomatic missions, deep space explorations, border patrol, etc. happening at any given time.
Over 150 member planets spread across 8000 ly's (and 1 Trillion lifeforms in the Federation) and this is supposed to be their entire SF armada?
However, it's conceivable that after the Dominion War Starfleet downsized as a "peace dividend."
After World War II, the US downsized the US Navy, including decommissioning and scrapping the USS Enterprise (CV-6). Maybe in a post-scarcity society where you don't have to worry about resources in the same way, things might have been different.
Also, when Starfleet was more in a pre-Borg attack peace era, the loss of 40 ships at Wolf 359 was considered a significant loss. So there might be some fluidity to Starfleet's numbers and how many times have we seen episodes/movie plots that revolve around the Enterprise being the "only ship" within interception range?