No, for AQHA shows, I think there is a set distance that is the same for each horse, right? IMHO, that would be more sensible cause it would also demonstrate that you had the ability to shorten or lengthen your horse to adjust to the obstacle.
I don't know if maybe setting them a few inches higher so that they really have to pick their feet up would help or not. It has been a long time since I had to ride a horse that wouldn't. Maybe going out on some semi-challenging trails with deadfall and hills would help them to remember to pick their feet up, I don't know.