You seem to think that one has to be either behind or ahead of the motion. That is incorrect. One can be with the motion and the only way to do that is with a balanced seat where the heels and the CG of the body happen to be in vertical alignment. For flatwork, that means shoulder, hips, and heels in a vertical line. For work over fences that means that the shoulder will be ahead of the CG, the hips will be behind the CG, and the heels will be directly under it.
A chair seat is inherently unstable and you need to be able to brace on something to stay on. Which is why western and australian saddles have huge, vertical cantles, pommels, and polleys.
If you are balanced and centered in the saddle you need none of that, as evidenced by the many riders who stay on their horses while cantering, jumping, and galloping cross country (not on manicured arenas) on english saddles during horse trials, fox hunts, and while just riding aggressively.
And there are many fox hunts out west that ride the same country that your cowboys do at a pace that would fry most people's brains.