Point taken. I still wonder if stilts are the answer.
A walking chair rather than a rolling one would be the equivalent of stilts, though not as far off the ground as traditional stilts.
Wheels seem to me to be the way to go, because they can be designed to go into difficult places with a certain degree of stablility. At the very least, except in the accident you describe, both wheels always remain on the surface. With a walking object, two of the four legs would have to be off the ground to take a step, like a horse's are. The rider would have to be balanced by the machine, which, unlike a horse, wouldn't have independent judgment or self-preservation to guide it.