Take place just on the Bridge? Is there going to be something on the viewscreen and out in space? Are you going to have a full bridge crew? Not go out in shuttles or have transporter or other effects? Yes, when you sart up a show, you often get a bigger budget for the Pilot, but, that Pilot Budget needs to build everything you're going to use in the first 5 - 9 episodes, or you're gonna have no cast or nothing but Bottle shows.
Professional American TV Productions are expensive, especially with effects and set dressing and Long hours, paying overtime on effects houses as well as personnel inhouse (Cast and Crew, Writers, etc), makeup, etc.
You could probably redress the sets after a Season or maybe at a mid season break, but, to bounce around between 3 or different ships and crew week after week. I believe that is going to be far more expensive then attractive for the expected viewers/ratings (HBO and many of the Pay Cable Channels, for instance probably wouldn't want it without soft core sex and/or foul language, and Star Trek isn't likely to be an "R" series, especially not if it's the only Trek Series running, maybe
if there was more than one running. Commercial Network or Basic Cable isn't going to have a healthy budget of $3+ Million an episode