Thank you everyone thus far for keeping this a civil debate.
So as someone who has been vaulting for several years now, I can personally say, I would stick to the no helmets in vaulting. As a vaulter we are trained to be quick on our feet. We literally practice emergency dismounts on the horses and barrels for being able to save our selves from landing hard/ sticking a landing. We practice being able to roll out if need be in all directions on the horse. Since we aren't sitting on the horse the majority of the time, this gives us a better chance of rotating a landing or fall.
Yes, I understand the risks, but from the research I have found so far on the rules of no helmets is that there are many concerns when a helmet is in play. If a vaulter were to fall in a way that they may face a spine injuries, a helmet could actually cause more damage to the neck/spine area. The head is protected but the helmet may cause a more serious injury to occur in the neck.
Helmets are of course designed to stay on our heads at a tight grip. Now image a group of 3 vaulters on a horse trying to perform and one vaulter accidentally catches this fingers in the helmet's harness or grabs on of the other vaulter's harnesses if they were losing balance. Right there is one major concern as we have others with us on the horse at times, and something getting caught in the straps would prove to be a dangerous situation.
And vaulters perform moves like chest stands and shoulder stands. A helmet can cause a vaulter to have less of a center of their gravity when trying to balance these moves (of course if one is used to it, it could become easier in practice), none the less the straps could become caught on the surcingle itself.
Yes, vaulters fall, yes they get hurt, but most often these are not head injuries. Most injuries are legs, arms, ankles, muscle, etc. Oddly enough vaulting is actually the safer of equestrian sports. Horses are well evaluated before becoming a full fledge vaulting horse (safe reasons are highly considered when looking for one). And they are in somewhat more of a controlled environment, as they are lunged in a circle. Sometimes a horse will spook over something, but we are trained to react as quickly as possible. Hence why we train emergency drills to help. And yes, our footing is soft. Actually much softer at most vaulting location compared to a normal riding arena footing at times.