I concur with the 10 posters before me. Can somebody tell me why a ship counselor sat on the bridge next to the captain? That never made any sense to me at all. Or that there were kids on the ship.
There is a school of thought which says that Deanna's role on the crew is actually one of the most important, which is why she gets to sit there with the Captain and the Executive Officer. Look at the number of times Starfleet crews went mad in TOS (Captain Tracey and Commodore Decker being cases that spring immediately to mind, but there were others). The responsibilities of command were such that there was a great emotional turmoil that could engulf the commander, and often times (as with Decker) they could make decisions which were lacking in good judgement. The Counsellor's role is arguably to keep tabs on the Captain's state of mind, and certainly Deanna openly questions Picard on more than a few occasions (sometimes in the Ready Room, sometimes very publically on the bridge). Even as late as Nemesis
Picard still declares that a ship's counsellor is a statutory requirement for the effective running of a starfleet vessel, and that just because Troi is running off to the Titan doesn't mean she won't have a replacement.
which Troi plays in the character dynamic of TNG was basically played by Doctor McCoy in TOS. But McCoy isn't nominally a bridge officer (although he spends more than enough time hanging around up there -- hasn't he got a job to do in sickbay or something?
), so he isn't theoretically going to always be there beside the Captain in the most high stress situations. Troi is right there all the time.