Hi Eric. How about spiritual-based explanations for physical exercises?
Spirit is spirit, mind is mind, body is body. They're always connected but how often are they in harmony?
Of course you can analyze the physical effect but by limiting yourself to the physical only then you may never find the real why.
Just being aware that there is a mental aspect and a spiritual aspect means that as you train and come across realizations then you can acknowledge them for what they are and gain a deeper understanding of what you are doing no?
Graham, the whole mind and body in harmony thing comes from the traditional observation about qi, jing, and shen (just like the Japanese "shin"... it's all borrowed from the Chinese). What they mean by "spirit" is not really at all like the "spirit" we use in "Holy Ghost" or something like that. It's more akin to "a fine, noble, spirit" in terms of alertness, focus, etc.
The pertinent saying about mind and body is basically that the desire to do something (this comes from the "heart") triggers the mind, the mind triggers the qi/ki, and the ki/qi triggers or leads the actual application of strength. This is "mind and body coordinated". It refers to a type of coordination in human movement.
O-Sensei understood this relationship because he was raised on reading the Chinese classics. The use of the mind to lead the qi to lead the strength is what he referred to in his douka as "the Divine Intent" or something like that. It appears that you are appending some different perspectives to the whole mind and body thing.