I was thinking about this earlier, and during a lot of missions there's apparently a bunch of really cool stuff that goes on off-camera involving your own ship or away teams. "Cutting the Cord" is one that immediately springs to mind, in which while you're away your ship is participating in the major, decisive battle.
It would be nice, at least on rerun, to take control of your first officer, or even retain command of your ship and simply send an away team, and experience the "other side" of these missions. That would definitely add replay value to missions that hadn't much before beyond mission rewards.
I don't know about taking control of your first officer, but fighting in orbit while your away team is completing a mission on the surface sounds nice.
I think it would be nice, and add a lot of depth and immersion to the game. Especially if it's limited to mission replay, so while you've already experienced things from the viewpoint of your captain you can see what your ship (or anonymous away teams) have been doing in the meantime.
Plus, it would be a way to avoid away sections of missions for those of us who aren't particularly fond of that aspect of the game.
It would also make for a great prelude for an expanded BOff/"personal fleet" system through which players of Admiral rank or higher could promote bridge officers to Captain and give them command of other ships the player owns -- either by converting them to PC's that start at rank 30, or making them (constant or ability-summoned) space combat "pets".