I don't think the pic changes the thrust of my argument. The emblems are not ship specific. If you want to use 1st Fleet, 2nd Fleet, etc., instead of ComSol, ComEridani, etc. that's fine. But they're clearly not ship specific.
1st Fleet, etc., fits with similar dialogue we've heard on DS9 during the Dominion War. And if there's one thing the military loves, it's tradition.
So, under this scheme, we've got the starburst pin representing Starfleet Command itself, the silver variant for the Academy, and four specific Starfleet insignia for starship personnel:
We've got the traditional arrowhead, the rectangle that we saw on the Exeter, the curly-Q one on Commodore Decker, and the boomerang on the crew of the Defiant (btw, on my 27" television, you could just barely make out that the dead redshirt in the Defiant's sickbay even
had an insignia, and I think it's pretty certain that a mid-60's Zenith 19" console set would be even less distinct, so I'd give them a pass in this instance; they tried to obscure the insignias and for the most part they did a damn good job. If that's not good enough, let's just say he was a recent transfer and hadn't gotten around to switching all his uniforms yet).
So, the argument can be made for at least four designated fleets. For the sake of argument, we'll say the Enterprise is assigned to First Fleet, with Starbase 11 as their local command base, hence why so many others are running around with that same insignia while not being assigned to the Enterprise.
That work for everyone?