I don't think big horses on the average suffer more than minor bruises when they collide with a lone human. They're big animals with strong bones, decently thick hides and lots of muscle.

Anyway, at least the couching technique used in the Middle Ages flat out required the presence of both a relatively specialised war-saddle and stirrups to keep the horseman seated (the Europeans developed these into very distinctive and specialised forms over time); the whole point of the technique is to push up the "break point" where the lance starts sliding back in the user's grip and is no longer being driven into the target by the momentum of the rider-horse combination, ie. where the impact power begins to go to waste. Obviously, that requires some "technological assist" for the rider to not simply slide over the animal's back as there's no way he can grip its flanks with his legs hard enough...

Thus, not really an option for the Classical lancers who in the beginning didn't even have saddles to work with. Also, I understand the "low and back" grip has the benefit that it's relatively easy to extract the weapon from the target after impact by rotating the arm up and back.