The gap-tooth smile is such a part of the culture, and there will always be missing teeth, mouthguard or not. Players with mouthguards are spittin' chiclets every other game.
But it's not just about teeth and cosmetic damage. Boxers don't wear mouth guards to protect their smiles. It is, like you mentioned, to protect their brains and their jaws. That alone should be reason enough to mandate it. (And sadly, like helmet-- and eventually visors-- it will have to be mandated for their own good because they won't do it for their own good on their own)
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