This. And it has been true since the beginning (with TOS).
Wrong. The role of the ship's doctor in Trek has traditionally been that of the confidant, all the way back to The Cage. Kirk often has heart-to-heart talks with McCoy, like the one in Khan where McCoy tells Kirk to get his command back before he really does get old. Spock can not provide that same sort of worldly advice because he can not relate as closely to human wants and needs. There's an understanding there between Bones and Kirk that is unique to them. I think pop culture's sense of the importance Bones has eroded a great deal because DeForest Kelley avoided the limelight and he was the first of the main cast to die, whereas Nimoy and Shatner have remained ubiquitous and continue to riff on their roles.
McCoy's role was supplanted by Pike in JJ Trek, where Pike acted like the surrogate father. Maybe this was because they retconned McCoy to be about the same age as Kirk when he was older than Kirk in TOS. So apparently when the timeline split, McCoy magically got born later than in Prime continuity.