Pretty much what @RnMissionRun said.
In my opinion, nothing about Star Trek really feels suited to a MU. Once you have your game's 'Kirk' and 'Spock'-esque spots filled, there's not a lot for anybody else to be doing except having space sex.
Star Trek doesn't really strike me as having the 'background' to really suit a MU either. I'm not aware of any detailed in-depth systems for different Star Trek weapons or ships floating around or anything and don't recall any, so it's not like 'combat' will really be anything special. It doesn't seem like there'd be a lot of opportunity for plots outside of "make up a random planet and alien species" either, where Star Wars has a billion things you could do plot-wise.
I don't play on a Star Wars MU or anything, but....I really see 0 reason why if you want 'space genre' for a MU, you would /ever/ pick Star Trek.
Star Wars or Serenity or something else would just offer a hundred times more.
Star Trek as a MU would have literally nothing except --
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Storyteller runs a thing with some made up planet you're exploring/whatever. (The problem here is Star Trek feels like it pigeonholes you into basically only being able to do this one specific type of plot which drastically cuts down your pool of people willing to run stuff. WTF else happens in Star Trek?)
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You're fucking on a spaceship.
Other space settings just are way better suited to a MU environment.
Edit : As a movie series and TV show, Star Trek is great fun. As a MU, it just feels way too "narrow" in the scope of things for players to "do". Star Wars, you have space wars, bounty hunting, planet-specific wars, galactic crime organizations, jedi peacekeeping, jedi vs sith, sith plotting, etc, etc.
Star Trek is...find a new planet. Maybe have a war with the klingons.
The problem with 'war' as a thing in Star Trek, is it does not seem like those scenes would be anywhere near as fun to play out as they would in some other Space-themes, because the scope of the battle is "100 people on 1 ship, with none of them really doing anything" rather than "10 people piloting 10 different fighters, all doing something" and foot combat would pretty much be 'phaser guns pew pew'.