Tackle football is basically the only sport my kids are not allowed to play. I don’t talk about it because I don’t want it to become something forbidden and therefore cool, but if they naturally find their way there and start getting pushy about it, it’s one of the few things I’m prepared to put my foot down about with no compromise.
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.
Football, boxing... seem the top two to cross off. I think skiing is perhaps the third to cross off.