Fair points all, TCatt. And I've read a lot of the Trek games here over the years.
Another thing I think is interesting, since you mentioned it in your third paragraph; I was reading a discussion on...I want to say the ST:Adventures Reddit, on the pros and cons of NPC versus PC captain. My original kneejerk reaction was NPC captain all the way, but I've been ruminating on it - the thought of course being so that one player doesn't hare off and start expecting everyone else to follow orders. I realized that's an awfully quick assumption that someone's going to go off the rails, and really, if an NPC is the captain the players might also start expecting to be railroaded and/or being hand-held through the GM's special-snowflake story.
It's a weird balance that I'm having to think a surprising amount about. There's another game, the Sunless Skies tie-in, that explicitly sets up that the ship's captain is - R.A.W. - both not one of the PCs and actually out of commission in the narrative to avoid both 'player power trip' and 'relying on GM handholding', and the more I think about about it the weirder that particular solution is. Not necessarily wrong, just weird.
That ramble aside, guess I just have to knock their 'winning' mindset down a peg, I suppose; that's pretty much all going to be off-table discussion. Frankly I was a little surprised that there was as much interest in this from a relatively munchkin-y group, haha. And heck, if there's any life left in this place might try some episodes for playtest.