I think Enterprise D treats the SickBay as a Mini Hospital given how many surgeries they perform.Now I've always thought of the D sickbay as a quick clinic, you come in get scanned, get a shot or outpatint care. For long care, OR, etc, you have other areas, probably close by the clinic.
And there are extra SickBay's spread through out the ship in different parts staffed by different doctors that only a few ever get mentioned on screen.
Since Beverly is the CMO, she probably only has to manage her fellow doctors and nurses and maybe take an occaisional shift.