Every horse need a solid foundation. Riding other people's horses I am finding I am having to give horses in their teens and twenties the solid foundation they obviously never got. Luckily the ladies who help me ride like seeing what I do with their horses and they like the results I get even though I mostly ride at a walk. The horses I ride are WORKING at the walk, something they've obviously never been taught. Same with the trot when I have enough energy. (By the way I pay for most my riding, the ladies catch, groom and tack up the horses for me so I have enough energy to ride.)
I work on getting horses suitable for beginner lessons. Some don't make it, like you said, square peg in a round hole. But with my MS this is just about all I am suitable for in the training department, teaching a horse that even if their rider is shaky and unbalanced they still have to obey and do what the rider says. I do ask the horse politely though, otherwise it wouldn't work.
I enjoy the debate too. We've had some good ones here on Barnmice!