I think Star Trek's core concept is part of the reason the games struggle. Shooters may be fun, but they don't quite suit Star Trek, and other games such as puzzles and RPGs are a harder sell.
And yet, point and click adventure such as TNG A Final Unity worked well.
I'm sure something similar adapted to first person style gaming (just with LESS emphasis on senseless shooting and MORE on say brainstorming etc.) or combining the likes of TNG A Final Unity, MASS Effect, Bridge Commander and even Birth of the Federation into one game (all styles merged in one) could probably work.
Imagine the ability to influence Federation development ala BOTF style... then when you have starships, you can select few prominent vessels and pick to transfer your point of view to one of those ships... engage in space battles similar to Bridge Commander, and go on away missions such as you would in Mass Effect with clear dialogue, choices and how those decisions shape the game (beyond the superficial).