If you're worried about head trauma, just consider that football is being widely studied & reported upon right now. Look at the stats of basically any contact sport: wrestling, soccer, hockey, etc. You'll probably have to dig deeper to find the the studies, but they all show that the athletes are significantly more likely to develop these types of brain disorders.

This is incorrect. I can tell you offhand soccer and hockey both have lower rates of CTE’s, soccer by a significant amount. American football has been the most studied and reported on because of how bad it is and how popular the sport remains anyway