Why is it that when a dog runs an agility course, the dog gets a prize, but when a horse runs a show-jumping course, the rider gets a prize? The dog has a trainer on the course telling it where to go; the horse has a person on its back telling it where to go. I don't see the difference, except that the horse has to do more heavy lifting.
Olympic rodeo would make more sense. There the person is clearly doing athletic work, not animal training.