Rugby is probably the best example for comparison.
The problem with rugby is that it is, well, rugby. The dynamics of the sport are completely different than American football.
You have any statistics on the accident rates for rugby vs. football?
Another great example is boxing. In the old bare knuckle days boxers got cut up something terrible.
But they didn’t wind up “punchy,” and true knockouts were uncommon. You can’t hit somebody hard enough to rattle their brain in their skull with a bare hand without breaking your hand.
So we made boxing neater and tidier and less obviously brutal for the spectators, and far more damaging to the participants.
As a female, I noticed that rugby players tend to have broken noses and cauliflower ears...
still better than brain damage.
Football was originally played without helmets by university clubs. The number and frequency of deaths from massive concussions led to the mandatory use of leather helmets before or around the turn of the century. Helmet suspension technology (along with size/speed of the athletes) has progressed but the human brain remains a soft gelatinous mass not unlike the inside of a chicken egg and there is not much that can be done about what happens to it when its velocity changes from 20 mph to zero in a fraction of a second from a hard counter blow.
A return to a soft helmet or one that absorbs and distributes impacts like the body of a modern car (damaged helmets would need to be disposable with a large supply of replacements available on the sidelines) would probably help and would also lessen impact trauma when helmets hit things like sternums, knees, and collar bones. But changing to "no helmets" in our style of "find somebody in the other uniform and cream him" football would actually produce on field fatalities.