Well, sabaku doesn't mean "move". It means something more along the lines of "handle/deal with/manipulate", so while it does mean things like "step to the left with your left foot", that's not *all* it means.
Though they often get glossed over at lower levels, and I've not seen any indications of a purposeful curriculum for teaching body skills directly, at higher levels, there seems to be lots of attention to small details that affect how one moves and generates power: tension in the legs, alignment of the hips and spine, etc. It wouldn't surprise me at all for kendo people to visit someone who moves well to see if they could learn how to improve their own movement.
It makes more sense to me if I think of it as body manipulation or even body handling.
If Ueshiba could get kuzushi from the touch at the end of a bokken, I think kendo people would be very interested in that. It wouldn't be the physical movement, really, that they would be interested in, but rather the body manipulations that Ueshiba was doing to get that kind of kuzushi on contact, even from the tip of a bokken.