Allen, I'll be the sacrificial lamb and get the ball rolling...
I was taught that aikiken and aikijogi should be seen along the same lines as the aiki taiso. The aiki taiso is intended to be a solo exercise to help one develop "aiki". Of course we hear phrases like "to get our ki flowing" and stuff like that which is not necessarily all that descriptive in any sort of scientific fashion. However, what was impressed upon me was that the aiki taiso are not to be done as warm ups, not as just movements, but as discrete methods of developing both the body to do "aiki" as well as developing better awareness of what is going on in your body. As we are a Ki Society offshoot, these things are assessed via tests to see if we are exhibiting our four principles to unify mind and body. So the taiso are to help us develop our abilities. And I was told that the aiki jogi and aiki kengi were intended for the same purpose -- additional "exercises" if you will to develop the same things. So we test for unification of mind and body thoughout these "kata" of sorts. We strive to keep one-point, etc. as we do the movements. Our stated goal is to better develop our understanding of "aiki" within our own bodies.
So, as with the aiki taiso add a stick with it's associated movements and style and you have new movements, new things to learn. Same with adding in a wooden sword with it's own associated movements and requirements simply gives another means to test ourselves, to develop, to improve.
So FWIW I view them not as kenjutsu or sojutsu or whatever. They are solo exercises to allow us to better develop that elusive feeling of aiki. So we focus on balance, relaxation and control while trying to develop the ability to strike/cut/thrust with power. For me it is being able to deliver a powerful strike with the jo, for example, while maintaining good form. That means the strike is using the as much of the body structure as possible to deliver that strike. Not swinging with the arms, but learning to connect throughout the body and use the ground, your legs, core, and arms with each strike. And then this is done from a variety of directions, angles, and styles that forces you to learn more ways of being powerful while maintaining the principles. Currently I'm still working on loosening up those tight hips. It's like a point of power constipation for me -- everything gets clogged up in the tightness there. But that's getting better slowly...
So, for me it is about learning how to generate powerful movements.
I'll preface that I have had a single aikiken experience, but have 14 years of both Seitei/MJER iaido expereince and kendo experience.
I think your post is rather on target with regards to what the whole point of that sort of practice is useful for. The waza themselves are not really all that important, even for kendoka who practice iaido. Its more of how to build the body. It seems like many others are going off on other tangents.
Its only recently that I had an experience where I learned how the cut itself through properly closing the body would result in it feeling as though my whole being slammed into my foot while cutting
. It was quite different than how many discuss fumikomi in kendo. It wasn't merely slamming my foot into the ground with my leg, or a good push from the rear leg, or using the hips, or dropping my body lower into the ground. With regards to "whole being" im not saying it in a spiritual sense, but rather in a physical sense. Quite literally my whole body drove into the foot.
As for test cutting, its pretty easy to do. Most people can do it on their first try even with no experience. If you click on the link below and select the battodo video, and skip to the 3:10 mark you will see a local reporter trying it for her first time at our dojo. (Note I am not a member of the batto do class).
That isn't to say that her cuts are good, just that it isn't hard to do unless you have poor hasuji. One can watch that video as well and judge how much arm/shoulder is being used by the regular class.