Originally Posted by rhosroyalvelvet
I don't know but show jumping horses as far as I know are broken and ridden away to be responisve horses that are sharp off the leg so they wouldn't really need one. And what if an awkward landing or take off left the stick in an awkward position and they had lost their contact a bit. It would be hard to gather both up and collect yourself in preparation for the next jump in time. I'm really not sure but those are the first things that would come to my mind.
A lot of them get caught up in the moment, if you look a lot of upper level jumpers have some pretty gnarly bits on, some even with bits and a hackamore. And riders riding at that level would have no problem collecting themselves while carrying a crop, I doubt they notice it much. They also need it, because if a horse isn't as responsive off their leg in even one part of the course it can make a huge difference, and not in a good way.