Ok, so I've read the reviews for the latest Star Trek game (the one with Chris Pine and Zachary Quinto as Kirk and Spock).  The short answer is it is terrible.
Yet I cannot help thinking that the reason is the kinds of games that they make that is the problem.
I would love to play a Star Trek game based on a single premise.  You are the captain and this is your first command.
Basically I want this.
1.  You create your character, RPG style.   Don't base it on any existing TV or movie show.  Have your own crew and characters.
2.  Map out the ship.  I want to be able to roam the hallways of my ship and go visit every room in the ship (of course going through doors can be a way to have a loading screen, i.e. every ship quarters you go into is the same room re-dressed).
3.  Put the setting before the orginal series.  Why?  Well, I think people like the old schlock with redshirts that die and mini-skirts as formal dress.  Also, keeping with point number 2 about having a full ship to roam this ought to be small enough to cut down the work to make that ship, but still large enough to be a proper ship.
4.  Oculus Rift support.  I can't help but think that people who have tried the VR goggles say a few things.  It can be sickening to move around too fast (aka combat), but it is great for exploring.  A Star Trek game would let you see some amazing sights, but the action 'combat' part of the game can be done while your character is sitting down in a chair and just looks around at people on his bridge.
5.  Co-op play.  I would like to be able to crew the ship together with my friends.
It wouldn't even need to be a Star Trek game per-se.  I wouldn't mind an RPG where you play a ship captain of any kind.  Mass Effect comes to mind, even if they use the combat of that game from Gears of War.  I think a sci-fi game setting with you as the captain of a major space warship sent off to deal with political hot spots would be fun.
P.S.  I have been known to do some 3D model making as a hobby, and I'm currently working on a small-ish Star Trek ship, complete with internal layout in a very basic way.  I keep thinking it would be fun to actually be able to crew this ship in a game.