The Volokh Conspiracy - How Federal is Star Trek's Federation?:

I would suggest that it is only Earth that is socialistic, while the other member worlds have free market systems or mixed economies. The human-dominated Star Fleet military is the only Federation military force, and is tasked with collecting tribute from the nonhuman planets for redistribution to Earth. But as long as they pay their taxes, which subsidize Earth's welfare state and Star Fleet itself, they are largely left alone to govern their domestic affairs as they see fit. The Federation is essentially a big protection racket (in both senses of the word: providing external security, and also "protection" against its own depradations).
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Why don't we ever see Captain Kirk or Capt. Picard on tribute collection runs? Because the Enterprise is one of Star Fleet's most advanced warships, and is therefore reserved for more difficult missions, such as going "where no man has gone before" in search of new wealthy star systems to occupy and tax. Note the term "no man," which further underscores human control of Star Fleet.

From Star Trek IV: The Voyage Home:
Dr. Gillian Taylor: Don't tell me you don't use money in the 23rd Century.
Kirk: Well, we don't.

I wonder if this asks too much of a federal system. While the Federation may not have currency, it definitely has commodities. While Starfleet may not be wholly representative, there may be many explanations beyond it being a non-federal protection racket. It may simply be that Terrans, being rather new to space exploration, are simply more gung ho. Perhaps the location of the Academy on Earth has something to do with it. It may be that in a loosely federated Federation, citizens of most of the planets would prefer just to go about their things as they always have.

Or, it could be that just like the chompers of "Galaxy Quest", much of the political foundations of the "Star Trek" universe are created ad hoc, when they're needed for dramatic purposes. That seems to far simpler explanation for the inconsistencies.