Part of the reason the show works is that we never really see Federation life outside of Starfleet. Mostly this is for practical budget reasons; what does a post-scarcity egalitarian society actually look like? That’s difficult to depict in a show designed to recycle the same set every episode and only very occasionally go outside to film.

So what little we see of the civilian federation looks… a lot like the US. There’s a president. Member states planets. Constant references to US history. A military that operates how Americans like to think their military works, rather than what it actually historically has done.

Newer shows take this even further. Section 31, as it was first introduced, was supposed to be a highly illegal, unsanctioned conspiracy acting in the shadow of the proper Federation. Now they’re presented as the ultra official, coolest badasses who are the only reason any of the egalitarian principals are able to survive.