It seems obvious that punches would be far riskier without hand protection designed specifically to cushion the knuckles and stabilize the hand, but I don't have any idea how much it would change the sport. To be clear, I am talking about a change to the unified rules of MMA, not a complete change to "anything goes in the streets."
I am hoping to get more practical evidence, and online searches aren't helping. The closest sport I could find was the Bare Knuckle Fighting Championship, but it disallows almost everything except boxing and still uses hand wraps. Warfare has always been primarily armed and armored, so that's no help. There are endless self-defense resources, but the takes are often conflicting, undemonstrated, or untested (to get a sense of how much BS there is, look up knife defense tests).
I'm looking for historical sports that approximate MMA minus hand protection (allow striking and grappling that target most of body) and an overview of their techniques, or personal knowledge from sparring and unarmed combat.