Re: Wrist Exercises
I think you're putting too much blind faith in the authority of people with medical degrees. Most doctors wouldn't know any more about this than the average exerciser. Only a tiny portion of MD's are well-versed in orthopedics and sports medicine, an even smaller subset of these will have ever thought seriously about the prevention side of things and the evaluation of athletic training practices.
On the other hand, I don't see how you need much expertise to see that this type of pushup is both hazardous and pointless. To start with, most people feel sharp, intense pain when trying them - even when attempting to load the wrist and get into position. That should be most of what you need to know right there.
If you have any awareness of the structure and properties of the carpal area you can see that this type of pushup forces an extreme stretch in the wrist extensors, and more importantly, all the ligaments and connective tissue that hold the lower arm bones and carpals together and all the tiny little carpals in place in between. This doesn't even get into all the nerves that are trapped and being pinched on the inside of the wrist at this angle. Perhaps you haven't had any experience with anatomical specimens before. When you handle a human wrist joint exposed and unprotected by the muscles and pain reflexes, it's easy to see that it wouldn't be much harder to pry the joint capsule apart than it is to break the capsule of a turkey leg.
The hand is your body's most delicate tool. With it you can potentially perform motor skills as fine as those involved in drawing on an egg or making jewelry. You need them to enjoy such things in life as eating, typing, sex, personal hygiene, making art... why would you want to risk trying to pry them apart with half your bodyweight?
On the other side of the risk/benefit equation, what is the purported benefit of the exercise? It isn't going to strengthen any of the muscles involved in doing a pushup in any way that is signifcantly different from regular pushups, or more similarly to a way you might use them... when do you need to push something away from your torso with the back of your hand with great force? In fact, this variation is much worse for strengthening purposes because wrist pain is likely to make you stop the set before muscle fatigue does.
The only possible benefits I can imagine for the exercise are desensitizing you to pain from excessive wrist flexion and increasing wrist ROM. In my book, however, neither of these is really a benefit. The pain reaction is there to protect the wrist from exactly what this exercise does to it: hyperextension which may result in ligament and/or nerve damage, and loosen the bone-on-bone connections which may jeopardize the stability of the joint.
Furthermore, I can't think of any reason to increase wrist ROM for Aikido purposes. What you need in ukemi is not more wrist rotation and flexion but the ability to react to forces that threaten the joint and move your body so that they do not take the joint out of its safe movement range.
If you really want to increase your wrist ROM or desensitize it to pain a little, do wrist bends as a separate exercise. I don't think there is any reason to even do this to this much lesser extreme. The traditional wrist exercises before class we've discussed are not done with anywhere near the intensity and duration for this purpose, and may serve as a useful warmup. Beyond that, why?
Regarding the pushup element, if you want to build upper body strength and shoulder stability, do pushups with a grip that is comfortable for your wrist, so that upper body strength is the limiting factor, not hand or wrist pain. In fact, I think it is better to do them on handles or small dumbbells so that the wrist can be kept in a stronger, more neutral position during this exercise.