We really don't talk much about the swings of folks I work with who are currently playing tournament golf.
But, in this case, maybe just for a hour or two, I'll make a small exception.
Here is why.
Great swings that travel on a "relatively" steeper EVENTUAL plane toward the ball (think Calc/Nicklaus), as opposed to Sergio/mid50's-60's Hogan, who swung to the ball on a relatively flatter EVENTUAL plane toward the ball, they need a right shoulder that travels on a steeper plane, more or less parallel to that eventual plane. Hogan and Sergio's right shoulder move is flatter than Calc, Jack, or in your example David.
For the record, I have never really given a rats rear end about whether or not someone's head moves up or down in the swing. And to get the maximum
Pull Back-Run Up-& Jump, the golfer surely must lower their head. So that's why, even though all the experts have a cow when Tiger does it, you've never heard a peep about that here in the negative.
In my opinion, golfers SHOULD NOT try to lower this right shoulder, much less try to drop the head. It should be done by matching the right side bend to the release. And in the case of David, we do work on it a reasonable amount. When we do, we do it more from the pelvis moving forward and open, and lifting the belt line through impact.
If you want to further discuss these moves, let's use someone else, as it is a worthwhile subject, just not current clients.