The WSJ asks, "Is It Time to Retire the Football Helmet?" With the debate about football head injuries and CTE swirling, some are wondering if wearing helmets is actually exposing players to greater danger than if their heads were exposed. Though seemingly counter-intuitive, the argument follows well-established moral hazard reasoning that some have perceived in, for example, government bailouts for large financial institutions.
Moral hazard arises when an insured party takes greater risk because they know they are protected. In the NFL, that translates players making and taking more violent hits because wearing a helmet makes them feel invulnerable. The reality, however, is that the helmet protects only from direct trauma to the skull; the brain remains very much at risk.
Taking helmets away would certainly change the sport. Though it's hard to disagree that all things equal, players with helmets will play more aggressively than those without, not everything would stay equal with that rule change. I suspect the game would evolve to resemble rugby - a sport not without its share of head injuries.