That sentence doesn't make sense. Starfleet isn't even "really all there is" even within the Federation, any more than the Royal Navy is all there is within the United Kingdom.
For all intents and purposes, the Royal Navy is "all there is" as far as the UK's naval forces. It is NOT, however, "all there is" as far as the WORLD'S Naval forces.
.... you are not making sense now. Was the question I initially responded to about what the
Federation is, or was it about what the
galaxy is?
Neither. I was asking about the scope of the fictional universe in which Star Trek takes place, which has to do with, among other things, the nature of its political alliances, the distances involved, the ease of transport and exchange and how cohesive its individual members are with one another.
Which is to say, what "world" are we supposed to be projecting on the Federation when we imagine it? Is it the "world" as defined along anglo-centric terms such as to mean "Our country, and also our allies, and a bunch of people who don't like us" or "the world" in global terms to mean "a bunch of countries that includes us."
This is based on the false premises that accepting a certain amount of centralization in joining a federal system is the same thing as yielding to imperium
It IS the same when it comes to the centralization of one's military, especially if that centralization implies either the disbandment or expatriation of ones' own armed forces. You become part of a foreign empire the moment you entrust a foreign entity with your national defense, especially when it is implied that that foreign entity will value its own defense at a higher priority than your own (something Starfleet has been seen to do in nearly every iteration of Trek; they have this concept of "core worlds" which must be held at any cost, the most important of which is always Earth; everyone else is seemingly left to wonder).
This ceases to be an imperium when one of two things happen: either the member states give up the REST of their sovereignty (in which case they cease to be autonomous and become merely territories conquered or annexed by the central government) or they retain primary responsibility for their own defense with our without the coordination or approval of a larger Federal-controlled force.
A benevolent empire is still an empire, with all the political implications that come with it. So if you wish to avoid those implications, you would have to either envision the Federation as a collection of worlds close enough and similar enough to yield to a central government and become a cohesive superstate (much as the 13 colonies originally did in the Americas) or you would have to concede for separate member states maintaining their own space forces spread across the galaxy, serving the priorities of their homeworlds. Otherwise "Starfleet
alone is the Federation's military" is to concede that the Federation is a benevolent empire dominated mostly by Earth.
The Federation is a democratic union of democratic planetary states, which practices federalism. It leaves a great deal of power in the hands of its Members, but it also has specific sovereign powers itself. And it is not dominated by any one Member -- not even Earth.
Militarily, this appears not to be the case. That's the significant difference here. It could, certainly, be mere coincidence that both Starfleet headquarters, the Academy and all of the major construction and R&D facilities all just happen to be on the same planet as the Federation's headquarters. But it goes beyond coincidence that starbases and ships outside of Sol are overwhelmingly dominated by humans, and the few aliens on the crew turn out to be aliens with close human ties (and on two separate occasions Ben Sisko complains that Starfleet's standing policy on the Maquis is largely shaped by cultural norms on -- you guessed it -- Earth).
That degree of centralization isn't a feature of a Federal system; the capital may contain the administrative centers for both the government and the military, but never in (for example) United States history have we had a national army at the Federal level composed overwhelmingly of soldiers/ships/equipment produced in Philadelphia. You don't have a single state militarily dominating all the others; that's antithetical of a Federal system, because the whole point of the Federal state is that no one state can survive on its own and all have to share resources for their collective wellbeing.
Further, it is very clear that the Federation Starfleet is not the United Earth Starfleet
That's far from clear at this point.
The canonical evidence does, however, seem to imply that the Federation Starfleet is the UFP's only federal defense organization. It seems that Member worlds maintain their own forces in the same way that U.S. states have their own National Guards and State Defense Forces, but there's no indication that they operate on a Federation-wide scale.
This is problematic insofar as the Federation Starfleet is as highly centralized as it is vis a vis Earth. It's becomes more problematic if those local defense forces are depicted as having secondary authority to Starfleet such that the latter can become involved in a situation and tell the locals "We are taking control of this situation." If Starfleet has higher authority than the locals, this again trends towards imperialism. The only way to avoid that implication is to either distribute Starfleet's operational bulk more evenly, or to concede that lack of distribution as a result of Starfleet's being only one part of a larger whole.
The DS9 episode "Rapture" established that as part of Bajor becoming a Federation Member, the Bajoran Militia would need to be "integrated into Starfleet." Exactly what that means is unclear; my hypothesis, given the continued existence of the Vulcan defensive services established in "Gambit," is that the Militia would be integrated into Starfleet's command structure (i.e., they'd become part of Starfleet in times of Federation-wide emergencies when called into Federation service, the way the U.S. President can federalize a state National Guard), but still exist as its own distinct service within Bajoran territory.
That's possible, but the same implications apply as far as authority goes, given -- again -- the issue of military centralization. The British Empire did this for decades, using the local forces of its own colonies to fight wars on opposite sides of the world simultaneously, supplemented by regular troops from its own forces. The degree of control they exerted over their colonies was immense, and yet the 13 American colonies would still have been considered colonies -- and Britain still an Empire -- if they had held seats on the Parliament.
The thing is, only the King's government reserved the right to negotiate treaties and international agreements, as they did with the First Nations in the 18th century. Arguably, the agreement not to expand the colonies west of the Appalacians was one of the major triggers of the Revolutionary War, since it was made by the British government without the consent or input of the colonists themselves (which is more or less exactly what happened to the Maquis).
How you handle a foreign threat is a big giveaway for your definition. A federal system prioritizes overall national defense of all its territories; in the event of a foreign threat, it will tend to mass its defenses on the very edge of its territory to prevent the enemy from attacking its outermost/vulnerable areas. An empire grows out of a central point, so the response to the foreign threat is to use those outer territories -- and even some of the inner ones -- as buffers to absorb the enemy onslaught or at least keep it at a distance until a compromise can be reached that the central government finds satisfactory (even if the outer territories hate everything about it). If Starfleet can be taken at their word and Earth really is the most important world in the Federation, then the Federation is an Empire in all but name.
Of course, the Klingons have said EXACTLY this on a number of occasions. "The Federation is nothing more than a 'homo-sapiens only club.' Present company accepted of course." And earlier, "Vulcans are the intellectual
puppets of this Federation!" Both the Klingons and the Romulans seem to believe that Earth -- and humans in particular -- are the heart of the Federation, and moreover, they firmly believe that the destruction of Earth would bring the entire Federation crashing down. Maybe they know something we don't?