There's amble on-screen evidence that all the ship "needs" is one person to operate her. It's when things start need repairing that more people are required.
It wouldn't surprise me if the core "crew" of the ship was only two or three hundred: the remainder could be made up of a rotating cycle of mission specialists (both starfleet and non-starfleet) and their respective spouses and children.
Conversley the ship's "crew" could be 950 and the score or so of children and confirmed non-Starfleeters (was it ever categorically stated that Keiko was never Starfleet?) that we saw on screen was all there was on board. Admittedly given that we know at least Jennifer and Jake Sisko were on the Saratoga, a much smaller ship, this is quite unlikely.