This has long been recognized as an aspect of Bujutsu training. But the important thing is that the physical aspects can be shown to actually attain unity of movement but rarely has been I'd bet. Better than the happenstance of twenty years of training. Where some get it and most do not.
But the body training and the movement has actual use in fighting.
Consider the old addage of Suigetsu and why it is so often written about. Movement in grappling is fine, But movement.... with edged weapons was deadly. Suddenly...... Moon / water and the potential for ...instant connection of two entities.... has more relevance.
Since we're yaking abut this stuff, how we carry our weight and the movement through the spine, is as pertinent as the movement itself. And the result of this type of body movement is significant on contact. For those who train in grappling the displacement and movement potential, not to mention striking. And for me the Counter-punching potential become profound. I am told constantly that they can't see them coming. Even something simple as a double underhook and leg wrap can be nuetralized without moving. And the abiltiy to "hear" is far more real.
Since this is new to some guys I'd encourage getting into grappling to try your skills. Your going to find a whole new dynamic and potential there where skilled guys will simply not be able to get in. You will have their center on touch. Other commen things will be them locking themselvs up momentarily. And if they are astute grapplers they will dump out and change up continually trying to get in.
For those who are new to things, theres going to be a lot of fun to offset the agony of training.