They did in the NHL years ago. The Game Misconduct penalty. I think it was Clarence Campbell who instituted it. I could be wrong.
I don't see anything wrong with it.
While it's possible to pick up personal fouls from bad calls, it seems the idea here would be to eject someone for two flagrant personal fouls. This would be a good rule for guys like Burfict or Suh.
there's plenty of room in football for good hard play. Dirtbags should be discouraged from making plays intended to injure other players. Enough get hurt just in the regular conduct of the game.
This is about more than head injuries.
Or they could just lose a player for a set of downs, or drive. That could be fun.