I never got the impression that the Federation was so loosely organized... now, that may be my own biases getting in the way of seeing clearly, however, the idea of the Federation being more of a coalition than a
federation seems illogical to me.
Memory Alpha states "
The exact nature of the government of the Federation has never been made clear on screen. From the information available, the United Federation of Planets would appear to be a constitutional representative republic, similar to that of the United States, prior to the 1860s.The exact division of powers between the Federation government and the governments of its member worlds is unknown, though various episodes indicate the Federation placed great value on maintaining local sovereignty over local affairs. Member worlds were left to manage their own governance in accordance with their own traditions and local laws, so long as the general requirements of membership were met, similar to how the member states of the European Union are bound together today.
However, Federation law did grant the government emergency authority to override local governance and declare martial law on a member's territory. (
TNG: "
Force of Nature";
DS9: "
Homefront")"
Additionally, it says "The
Federation Council was the unicameral legislative body of the Federation. (
TOS: "
Amok Time") Composed of representatives from the various
member worlds, the Federation Council held the power to create, amend, and ratify Federation law. (
DS9: "
Rapture";
TNG: "
Force of Nature") The Federation Council also held a great deal of influence over the operations of the Federation's military service,
Starfleet. It sometimes served as the judging body of specially-convened
courts-martial, and on occasion issued operational orders to Starfleet. (
Star Trek IV: The Voyage Home;
TNG: "
The Defector") The Council also held influence over the making of Federation foreign policy. "
Now, while Memory Alpha seems to indicate that the Federation is in fact somewhat loosely organized, it also puts forth the idea that is a representative republic, which is certainly more coalescent than the EU or UN. In addition, while local sovereignty is maintained, Memory Alpha makes clear that the central government could take executive control over any area of territory if it so desired. While various species may be able to depart the Federation, as members they surrender a significant number of rights to the body as a whole.
I certainly don't think the individual states have their own militaries. It seems Starfleet represents the Federation Council's interests, and consequently all of the various states. During the Dominion War, we saw nothing but Starfleet vessels in service. There were no uniquely "Bolian" or "Vulcan" vessels, for example. In addition, during the Dominion invasion of Betazed, Sisko discussed only the Starfleet task force which had been out of place. He mentioned no Betazoid forces which could potentially have resisted attack. This would indicate that the member worlds have no military vessels of their own.
If member worlds give up their military forces when joining the Federation, certainly a great deal of sovereignty is being surrendered. Without military forces, their best bet at ensuring that a collective fleet served their interests would be in further integration with the central government, and increasing the legitimacy of the Council, through expansion of its powers.