Medical is considered Science, so you can skill out a Science officer with all medical skills, if you like. However, no doctor from TNG on, served an actual function on the bridge. Besides The Doctor, when he went all ECH...
Actually, to add to that, McCoy never did much on the bridge either, except advise Kirk and get knocked around when the ship was tossed about. Crusher did stand watch on the bridge in the center seat, but that wasn't manning an actual station.
I play from the perspective that my Federation Science starship - regardless of tier or class - is assigned to Starfleet Medical. I maintain two Science Boffs at the moment. The higher ranked one is more skilled in the broader ground sciences (Tricorder Scan and Gravimetric Shift, for example). My secondary Science Boff is focused upon medical ground sciences (Hypospray and Medical Tricorder, for example).
My Science Captain is equipped with a Medic Kit. So also performs ground missions as if she were a Doctor (well-trained in use of arms also ). I guess I had Dr. Crusher in mind? Whose career went from CMO to head of Starfleet Medical to Captain of her own starship.
The styles of a ground mission determines the make up of my Away Team. Sometimes I compose a science team with only Science and Engineering Boffs.
The "science" BO, represent to "medical", "science" and "counselor" (or medical "mental" and social advisor) departaments. In the Kirk era, McCoy and Spock take that works. In the TNG, more chars take his own works.
Maybe, science BO must give any skill to recovery crew, more that tactical BO (that officer (tactical), can take the "boarding parties" more that engineer). And engineers can take "control" over tractor beam, more that command the boarding parties.
It is ilogical. The ship with a great odds to generate powerfull tractor beams, depend from a "secundary" BO (science) for it ship. Not from his "primaries" BO (engineers).