Aw hell, I've seen plenty of adults that couldn't control their horse any better than a small child.
Also, most, if not all, of the horses that you see these small children on in rodeos are 'bomb proof'. Most are 18 to 24 year old veterans of the rodeo circuit and if you take notice, you'll see that a lot of times these small kids are just on for the ride because the horse knows the pattern.
The world is a dangerous place and people die. Some sooner than others.
It's the kids riding outside the arena that I worry about with all the distractions: other horses, trucks, kids running, carts, and who knows what else.