That poses interesting thought about the Federation in general.
Are member countries happy to join, then have their own space fleet disbanded in place of a largely human fleet headquartered from Earth? Personally as a member state I'd fear if they'd defend me as much as Earth. Particularly in an invasion, are they going to save me before Earth?
You could have interesting counter dynamics. Can Federation worlds basically join up and then sit back and think they're protected without contributing anything? Could argumetns similar to what goes on with NATO about certain members not pulling their way take place on a Federation level? Should there be quotas - like a certain amount of the planet population needs to go into certain areas such as defence of the Federation?
For my part, I liked how the FASA gaming Trekverse played around with the concept of membership. This was mainly during the TOS/TMP era with only a little bit of the TNG era added in before FASA lost their license from Paramount. They generally tried to be consistent both with the more limited canon of the early 80s and other sources that were considered to be official at the time, like the Spaceflight Chronology and the Franz Joseph Technical Manual.
The FASA Federation, in keeping with what TOS seemed to hint at, is kind of more like a galactic U.N. There are four main categories, full members (such as Vulcan and Andor), associate members (with fewer responsibilities and more limited voice, but who might eventually transition to full membership), colonies, and protectorates. Troyius and Memory Alpha are examples of associate members, while Halka is a more rare example of a fully independent world with Federation ties.
The Federation Assembly (which provides central government and creates legislation for Council ratification) has two representatives from each full member and one from each associate member. Rarely, protectorates and colonies can have special non voting representation on world-specific matters, but it's uncommon. The Federation Council, which implements Federation policies, treaties and oversees Starfleet (among other duties), has five permanent seats for the founding members and a rotating group of six seats for other worlds, chosen by popular vote and confirmed by the Assembly.
Not all of the planets within the Federation are comfortable with how full membership might impact their cultures, and some prefer the minimal level (associate, colony or protectorate) desirable in order to share some of the benefits of protection from enemies like the Klingons and the technological advancements. Being auxillaries in this context means the potential benefits aren't the same as for a full member, but that's also an incentive to consider that option one day.
Starfleet, as an exploration and military body, is generally subject to local laws within a star system (although this can be overridden in special circumstances, if the mission is considered extremely vital to Federation interests), and many worlds retain their own currency which can be exchanged for the standard Federation credit. This was long before the "no currency" goofiness.
The Andorians are a major factor in the production of some of the fleet, and the Vulcans also make smaller contributions primarily in the exploration branch. Andorian contributions are more military, with the Tellarites mainly contributing in engineering and support.