Sure seems like with the emphasis put on safety the last few years, that having a mouthpiece in during plays would be required by rule. As alluded to here, and may times before, the hits taken are brutal, and for anyone who has worn a mouthpiece before, it doesn't take a scientific study to let you know that it helps absorb and cushion the impact to a degree (and the mouthpieces now are a lot better than they were years ago). There's a reason the ref immediately steps in and temporarily halts boxing and MMA fights when a fighter loses his.