I only feed live to my snakes that absolutely refuse everything else--and I stun any older rodents that get fed. Yes, they most certainly can and will damage the snakes. My live-eaters already have a few minor scars because they just don't grab the rodent right each time. (The albinos are particularly bad about it, and I have to balance offering them unconscious prey--which the female wants to turn her nose up at, since it doesn't move--and getting the betadine ready if the rodent isn't out of it enough, and bites).
There just isn't time to get forceps in there to intervene if the snake wraps the rodent with the rodent's mouth against its body. (I keep trying, but those two just won't take prekilled--or even live off of forceps, and it's been a year).

Any nutritional argument you could make about f/t can be solved by feeding pre-killed, or stuffing a bit of brewer's yeast into the ft rodent.

I am not entertained by feeding live to the snakes that won't eat dead prey--I am generally anxious. I don't want them to get hurt.