So when you punch, kick, throw, walk or pretty much do anything while standing up, do you feel a sideways weight shift?
Try simply walking forwards very slowly. When you pick your foot up off the ground, do you feel yourself start to shift/lean over to the other side? Try the same thing with both feet together, and pick one foot up and set it down shoulder width without falling onto it.
What happens if you don't get that shift? Whats the martial value in it?
I find training something like this a heck of a lot harder than waza practice.
walking is basically controlled falling. The martial value in not moving via a controlled fall is that you center is never pitching in the direction you want to go, making it harder for someone to take advantage of your momentum. I would agree about the waza comment and also add that focusing on moving that way makes waza both easier and harder.