"Safe" is a strawman, and "not to a meaningful degree" is simply a lie. Fewer serious injuries is meaningful.

That being said, rugby is a different game. Football for the most effected players is one crushing impact per down, and a lot of waiting around and planning. Without helmets, half of the players would be knocked out cold. Rugby is not like that.

Every down in football is basically like a sumo tachi-ai (initial charge.) It's absurdly stressful without a helmet to do it even once a day between professionals. People would have to stop leading with their heads.

> If people just liked the violence

This is irrelevant. I love gridiron football, I think it's the best team sport ever invented, especially for spectators. I don't just like the violence, I like the violence. I have to accept the fact that I might not like it as much if people weren't leading with their heads. It's also the smartest game in my opinion, and I'm amused by upper middle-class people in the US thinking that "soccer" is classy (because Europe) when all the players are so much dumber (let's talk about heading; that ball is soft, too.)

American football is an atrocity, though. Even at the professional level, it doesn't pay enough for how bad it hurts you (and careers are shortest for the people who see the most impacts.) At the college level, forget it.