Two reasons.
Psychologically it establishes the bridge crew as the most prestigous officers on the ship. Whereas we never see the poor schlubs assigned to the "bottom".
If you look at the two pilots of TOS, the opening "curtain" is the viewpoint swooping up the the top center of the saucer and then the cast is revealed through the figuratively invisible ceiling at the top of the dome. This may have been the intended way to open up Star Trek episodes which would have necessitated the bridge being on top.