Sorry I'm late about getting back on some of the questions and comments:
Colas-Thanks for the +1. I have admired your surfing for years.

Kisutch- I agree that this maneuver can get you in a countered position that conflicts with the original question. I just wanted to point out the key difference in the paddle action between burying the blade to pry the turn around, or planing the blade behind you so that you can do a more extreme layback using the rail to create a sharp and powerful turn. I agree with your point that there are variations depending on speed. As you point out, you can blend the paddle blade options so that the turn may start by reaching forward to plant the blade before the wrists flip over to plane the blade around behind us. For a long time, I made the mistake of planting the blade out in front and keeping it buried throughout the turn which prevented me from really laying back on the rail as the turn evolves.
Saya suka SUP-Thanks for bringing up the Blane Chambers video as a good example. The paddle action I am talking about during the cutback involves wrist flexion with the knuckles rolling downward so that the convex side of the blade is skimming the surface behind us. We can see this in how Blane's wrist changes from bottom turn to cutback. During the bottom turn, we see quite a bit of wrist extension (knuckles up), often exceeding 45 degrees. As he comes off the top, we see this extension disappear and go somewhat into flexion which is not as obvious in part because many of us have much less range of motion in extension than we do in flexion. The top hand really controls the blade angle much more than the bottom hand and at least in my case, it often turns the blade angle more than my lower wrist can keep up with so the top hand may be turning the shaft in the lower hand. My goal is to get the blade parallel to the lip so that it planes on the surface with maybe a slight tilt up of the leading edge to be sure that the blade continues to plane and does not dive.
A great way to get the feeling for blade angle and wrist action is to practice while standing around in the lineup. Play with skimming the blade quickly back and forth along the surface on the convex side of the blade. The part where the blade is moving back along the water imitates what I am talking about in the cutback and you can even play with swinging the blade all the way around past the tail of the board to get the full feeling. If the blade dives instead of planes, then we need to roll the wrist more to keep the leading edge climbing above the surface instead of diving. You can also practice this when bracing while riding downwind bumps on a SUP. Bracing with the paddle behind your back during a downwind glide is the same paddle and wrist action as in the cutback we are discussing. This behind-the-back bracing is also common when a snap off the top leads to dropping down with the white water and you will see the pros really sitting on that blade behind their back for stability in big whitewater.
Thanks for the conversations!