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.
Funny, I don't walk like that. I walk like those walking robots ... front leg pulls the back leg forward while driving the back leg heel as it leads the movement forward. As the once rear leg moves to the front and touches the ground the weight shits to that leg - repeat. No falling only what looks cumbersome is remarkably stable and very difficult to hold me back or prevent me from walking by pushing from the front. I can smoothly drag people (or dumb loads, too) along or plow them out of the way - or both. I do tend to have a sideways weight shift but I'm working on making that smaller ... baby steps.
Of course, I'm large and scarey looking so maybe they are just getting out of my way on their own accord.
Walking is very fruitful ground for investigations of all kinds.