I've always thought this was a silly point in TOS, and was glad they fixed it with Dr. Crusher in TNG, who mostly does appropriate medical things, she doesn't hang out with the captain on the bridge. Just another thing, like Kirk constantly beaming down with away teams, that looks silly when you think about it.
I simply liked having McCoy on the bridge. If Crusher had been a stronger character it would've been a crime to keep her down in sickbay.
In universe, at that stage of his career McCoy is likely more in an administrative position that doesn't require him in sickbay constantly.