Although the starfleet crews we generally see in ST are largely human (for TV production reasons), an in-universe explanation for the prevalence of Earth Starfleet type vessels (and generally human crews - OK you could have identical non-human humanoids too) would go right back to the founding of the Federation. My theory:
Earth managed to get allies to help with fighting off the Romulans. Therfore Earth needed the others, more than, say Andor, need Earth. Hence the agreement behind the Federation was that Earth would put the most materiel and personnel into the fight (and later the Federation). This, although allowing the other races to reap the rewards of the alliance - but not risking too much, would later work massively in Earth's favour, with the running of Starfleet (and effectively the Federation) being controlled from Earth. Hence in ST6, the Klingons call the Federation a 'homo-sapiens only club', because of the prevalence of humans in the Federation.
Second, going back to the founding of the Federation, given the long cold war (with occasional flashpoints) between Andor and Vulcan, and the peace process assisted by Earth, these two worlds agreed to disarm in order to foster trust on both sides. The existing ships (that survived the Romulan War were probably partly absorbed into Starfleet under a mixed command crew structure and the rest scrapped. Just like on Earth, there are stll treaties limiting the military strength of Japan and Germany, even though the conflicts that forced these treaties are well into the past, the Andor - Vulcan disarmament treaty was probably never fully rescinded, leading to a significantly reduced participation in Starfleet by these races.
I would also agree with the assessment that Federation member worlds that had a 'Home Guard' fleet before joining the Federation would probably keep this to some extent, a bit like a coastguard fleet, but not with the power to do much more.
When a new world is taken into the Federation, where possible, manpower and equipment would probably be absorbed (except for the 'coastguard' role, but would be phased out as an independent force. Bajor, for example, the militias would need significant retraining to function in the Federation military structure, and their kit was outdated and probably on its last legs, so likely headed for the scrapyard (and a few museums) fairly quickly.
We know that the N? prefix denoted a vessel under Federation government ownership, as opposed to private vessels / commercial vessels belonging to someone based on a Federation world, or even planetary coastguard vessels. I would consider it likely that on the absorbsion of a new member's military into Starfleet, any vessels brought in would be given an NCC number (if military) or an N? if another type. This could explain some of the massive numbering jumps, of at least 60,000 registries between TOS and TNG, with short-serving absorbed vessels.
A last thought on mixed-crew vessels, we know that Vulcans are used to a warmer atmosphere than humans and that andorians for example are used to a colder environment. Although quarters can be environmentally controlled to the user's preference, communal areas must strike a balance. An Andorian, serving on a mainly Vulcan crewed vessel would probably be unconfortably hot, and if a Vulcan would be unconfortably cold on an Andorian crewed vessel, so these arrangements are generally not used. Other species, we know, also have variable atmospheric requirements an also probably different requirements for temperature and gravity also.
In summary, this would seem to answer some of the discrepancies noted between the number of active vessels in Starfleet compared to the number ever registered since 2161, and also the presence of generally human majority crewing.