It already happened.
IIRC it was in a collage game between Harvard and some other school back in the early 1900's. It horrified people to the point that they began changing the rules to prevent it from happening again.
Back then the problem was a lack of protective equipment. Today it is a over abundance of it.
Take a look a Rugby a game that is very rough and tumble yet has less major injuries. The difference is that in Rugby you don't wear protective gear. So if you bang your head against another players head it is going to hurt. So you don't do it.
Something to think about.
Iowa State University’s Stadium is named after Jack Trice; he died from injuries suffered during a game: