Kevin Leavitt wrote:
what does all this stuff do for you, or what does it prove/test?
Unbendable arm, the Jo trick etc.
Well, essentially it makes you stronger and gives you and advantage over an opponent. Howe does it do that? I may have to ramble a bit, but I'll give it a try so that it makes sense in an obvious and practical way.
Think of a native porter carrying a load on his/her head. The load is allowed to go straight to the ground through the skeletal structure, so the main expenditure of energy is no longer holding the load up, but is only in stabilizing the skeletal structure so that it carries the load. Can you see the benefit? The load, if it could feel things, would feel this extremely solid support underneath it, while the native porter feels like he is getting a lot of carrying power for not so much energy expenditure.
Now let's just hang a load from a rope at about the head height of the native porter and let him get under it, align himself, and then straighten cleanly into the load with his head. The load will feel this tremendous force of the ground straightening into it from below and the hit will be devastating if the native porter kept a good alignment. This hit again was very powerful, yet it required mainly the straightening out of a structure that was simply conveying the ground to the load. Let's call a path that conveys the ground a "ground-path".
When you see Tohei of someone holding out his forearm for his uke to push on, he is actually doing a version of the native-porter&load thing, only he is "bending" his ground-path or forming a groundpath to his forearm. If you were to draw the actual path, it would come up Tohei's back leg (in most cases) to his middle, and then go from his middle seemingly across the air to his forearm. The path doesn't really go across the air, but the mind can set up resultant forces so that for all practical purposes Tohei lets a push to his forearm push directly into his hara. Tohei is essentially showing how to use the force of the ground or the force of his weight do his work so that his muscles don't have to exert so much brute power.
One of the cool side-effects of this ability to make force-paths is that you can get very sophisticated in your ability to generate these paths and you can learn to generate a path in response to an incoming force from an opponent and manipulate *some* of what he's doing by mixing your forces with him, borrowing his forces, etc.
The Misogi breathing, stretching and compressing exercises, etc., are a way of building up the myo-fascial structures in the body (think of it as strengthening something like pliable living rawhide by continuously stretching, contracting, working it, etc.). These structures in the body, as they get stronger, make you very strong. The saying is that "the ki by itself is not too strong, but ki with muscle is very strong". To keep it simple, let's just say it augments the force stuff in the first part, although it's a very interesting and complex phenomenon, on the whole.
A lot of ki demonstrations are simply to show that someone has developed these skills, not to show something that is particularly devastating in combat, Kevin. For instance, if Tohei can stand and show a powerful and solid path in the face of a push to his arm, you should be able to extrapolate that he can retract and store along that path and then suddenly push or hit by "straightening out the ground".... and that's the essence of kokyu power. He hits with the ground; an ordinary person uses brute strength. You could say, "yeah, but I'm a big boy and I can hit pretty hard anyway" and I would say "sure, but if you learned to use this stuff you'd be far more stronger for the amount of bulk that you have."
Anyway, that's a quick attempt at answering your question, Kevin. Hope it helps.