Notice how Kershaw Peter Pans off to his right after every pitching - regardless what that pitch is.
Well, let's take a look at those parts of his body that force a balance scenario after his release.
First off his pause with that stride leg may seem the reason- but it's not.
Watch his glove hand closely. As he finishes every single pitch at release, his glove gets tucked into his belt line. Couple this with his explosive power going forward, his pitching arm comes around and down, then his pitching hand ends up swinging down to his stride leg's knee. All of that shifting of weight and mass on the move- to his glove side, creates an off-balance situation for this man after the pitch.
Health reasons to be concerned with - I don't know enough about the man's history nor do I know enough about the man himself to make a comment.
However, it seems that Kershaw and those like him would be very weak towards the first baseline on the bunt.