I agree. I'm surprised they still have the standard equestrian competitions.
If 3-day and jumping huge fences are allowable, which really ARE dependent on the horse himself and is much more the object of the sport, then I think they could allow jousting. Much more dangerous for the humans, who are the object of the sport.
They will never allow this because of the humans. Tilting they would, not really dangerous at all and akin to archery competition.