It is a neat idea, but I suspect part of the problem is that you can control your ship from the bridge. They could put a periscope on the bridge, but I doubt you'd be able to sit down at it and start firing weapons for the same reason you can't steer your ship from the bridge.
To tell you the truth, I do not know if it is something they can do
Well, space and ground combat is so very similar in terms of mechanics that we've already fought ground missions in starships or spawned as characters in space (that was a fun bug ). And since Shooter Mode already exists for ground combat, it should be relatively(!) easy to port it over into space.
Nothing fancy, just ... when you're in a fighter or a raider press a button, your screen zooms in a bit, you get a "scope" effect like on ground, and your weapons are now click to fire.
You'd probably lose out on the ability to use lots of personal or BO skills (given that there's only so many buttons you could put into the action bar), but perhaps this can be compensated by a slight damage boost or weapons cooldown reduction (i.e. the same thing they did for ground combat).
Hopefully once the fixing/halfing of the kdf side is complete (if it ever gets done at all) they.will make a small team dedicated to figuring out a bridge view system.
They would need to rescale most of the bridges, add camera points, lighting and effects, tons of animations, and most importantly figure out how to do either a fixed and floating lock camera display for the main viewer, so you can have either the eyes forward cruising mode, or a mode following the camera with a little indicator as to the relative bearing/z of the enemy.
Oh. A bridge mode? I don't think that is feasible - aside from requiring an entire engine revamp (unlike in SWG, ship interiors in STO are their own maps right now, much like space, and you can't have a map move within a map) I seriously don't see it used much during play:
From how the game is structured, combat (which makes up the majority of gameplay) requires a certain degree of overview, and a bridge screen offers only limited perception. Sure, you could probably have it "lock on" to a single enemy like it worked in Bridge Commander, but in doing so you will still miss out on anything else that's moving in the vicinity - from enemy and friendly ships to fighters to mines and up to entire planets.
It just wouldn't get used, aside as a novelty for when you travel through sector space, and I don't think the resources necessary for an entire engine revamp can be justified with that.
What I'd like, and what seems far more reasonable, would be an option to remain on the bridge whilst moving in sector space. Just click on a destination in the map and have your ship go there whilst you stay on the bridge all the time. This is far easier to implement because (a) the only thing that needs to be there in terms of graphics would be a non-interactive animation for warp travel on your bridge screen and (b) you won't miss out on anything in sector space, so there doesn't have to be any kind of feedback whatsoever. Essentially, you will have a "ghost ship" moving through sector space whilst you remain on the bridge map, and when that "ghost ship" arrives at its target destination, your helmsman will tell you, and you can switch places with the placeholder vessel.