Did you watch DS9? Major Kira, Odo, Quark, and Garak - all major players in the show, but not a one of them in Starfleet. They interact with Starfleet on a regular basis, yes, but that is by no means the show's only perspective. Much of the value in the series, in fact, is stepping outside the all-Starfleet all-the-time view.
You may find it silly to use a Trek game if you aren't intending to have any Starfleet involvement. But, to many folks, playing a Star Wars game with no Jedi PCs seems similarly silly - after all, the movies and TV shows are set solidly surrounding the story of the Jedi. They are the similar raison d'etre of the Star Wars saga.
Honestly, the number of DS9 episodes I've watched could be counted on one hand, so I don't have a ton of experience with it. But I will say that taking into account just the different TV series, DS9 is the outlier. Pretty much every other TV series has a central focus on a starship, its captain and crew.
Also, "silly" is a bit too strong of a word to use regarding running a Trek game without Starfleet involvement. It's certainly viable. And there's no doubt that there are interesting stories to tell outside of Starfleet. But based on the bulk of the encompassing material, to me the general idea behind running a Trek RPG is that you're interested in recreating the experience of the officers and crew member of the U.S.S. Enterprise (or its fictional equivalent).
I just have a hard time seeing a GM, or a gaming group, sitting down and saying, "Hey, let's play an RPG in the Star Trek universe! Except we don't want it to be ANYTHING like any of the TV series where you're flying around in the U.S.S. Enterprise!" It's just such a core part of the seminal Trek experience. On some level the choice to play a Star Trek RPG seems to me an indication that the group WANTS to engage with the kinds of character-driven / procedural investigation driven / societal and moral thematics that are prevalent in the source material. If you don't want to engage with that "stuff," why do Trek at all? Wouldn't some other kind of sci-fi suit the need better?
And I think this would/should be reflected in an RPG system designed to work within the Trek universe. Something like Burning Wheel makes way more sense as a baseline starting point for a Trek RPG than anything remotely resembling D&D.
As far as the Jedi / Star Wars comparisons go, I know Edge of the Empire initially raised quite a stink on other RPG sites when people realized you couldn't play Jedi out of the box, and were going to have to wait 2-3 years to get rules where you could. It wasn't a big deal for some, but for others it was definitely "a thing." And Star Wars is far, far more amenable to writing Jedi out of the fiction than Star Trek is to writing Starfleet out of the fiction. There's never a large number of Jedi in any time period, but especially in the Rebellion Era and the time period shortly after.