Sure it is. So's rugby. But rugby looks like a "purer" sport. Maybe the equipment introduced into American football has spoiled the game.
I think the NFL plays on both sides. They want to prevent injuries while trying preserve some of the spectacular violence. I can't think of anything more violent, outside of NASCAR car wreck, than a quartback sack. The NFL has come up with these parsy rules about it. But if they want truly to prevent them, they could add another player on offense, or something.