From: http://www.time.com/time/nation/article/0,8599,2027053,00.ht...
The mouthguard is actually the key safety gear for reducing the likelihood and severity of concussion injuries. The soft headgear sometimes worn is primarily for protecting the ears during the breakdown and scrum.
The defensive side of American Football is very much brute force orientated especially for the larger players.
On top of that being probable, players try to hide concussions (resulting in compounded head injuries the next time), and players rebel against the NFL's attempts to legislate fewer dangerous head-related hits and tackles. Actually, even fans and the media have the tendency to pine for skull-crushing, cringe-inducing hits at high-velocity.
I could probably have summarized the problem in one word: "culture".