The thing is, some people like full contact sports. And not just watching them but doing them. If you stripped tackles out of football or body checks out of ice hockey, that would make it a different sport, not just for the spectators but (much more importantly) for the athletes. Nobody makes it to a high level in a sport without actually wanting to do that particular one.
Full contact but restricted martial arts also exist and mitigate risks by limiting the range of allowed techniques. Some of them do it in different ways than others. Judo is full-contact but disallows strikes, which makes it massively different than something with strikes. Semi-contact karate avoids the full-contact part, which makes it different in a different way.
Full contact practically always comes with risks, and full contact with fewer restrictions comes at much greater ones. Spectator expectations or other parts of culture may encourage the athletes to take risks and go to greater lengths than they otherwise would. But it's difficult for me to agree that modern society should have no place for sports that mentally healthy people actually want to participate in just because it comes with a risk of physical injury or intentional roughness. If they wanted to participate in a different sport, they'd have options.
In the end it's of course a matter of where to draw the line. Rather few people would nowadays want to allow fights to the death even if the participants wanted that. (Although, in reality, I don't think such a sport would get that many willing and actually voluntary participants either.)
It's weird though - I love watching parkour which is the riskiest of risky sports in some ways but when it comes to stuff like NFL I think it needs more regulation around head trauma.
I think if someone seriously injured themself doing parkour or base jumping (or bare knuckle boxing) there's an implicit assumption that people partook in that activity knowing the risks whereas with a professionally recognised high stakes sport (where the athletes may also have contractual obligations to perform) then there need to be higher standards and awareness.
For instance why is head trauma more of a problem in NFL than rugby when rugby players don't even wear helmets
My opinion: it's the padding on the other parts of the body (particularly the shoulders) that makes NFL so dangerous. If you ran directly into someone at full speed without padding you'd injure yourself as much as you'd injure them, whereas the pads NFL players wear allow them to use their bodies as guided missiles. Rugby collisions (generally) happen at lower speeds, where the intention is to wrap up and grapple the opponent to the ground, not blast them off their feet. (There are also on-side rules in rugby, and no blocking away from the ball, so many, many fewer blind-side hits occur.)
I don't know much about rugby (of either or any kind) but I'm under the impression that it has some kind of a culture of mutual respect. That might mean the players tend to exercise greater and more conscious control in taking contact despite the sport being rough.
I'm also wondering if that's partially connected to exactly the fact that they don't wear protective equipment. In many cases it's of course definitely helpful to have protection, but since it can also make the risks less obvious, using heavy padding might also encourage heavier contact. If, on the other hand, none of the participants are under any illusion of safety, that could discourage recklessness and perhaps even encourage a sense of mutual respect.
Helmets generally don't offer that much protection from concussions. They do reduce the risks of other serious head injuries such as fractures, as well as more superficial injuries, but if helmets make people think they can take heavy contact with abandon, that might increase the number and severity of concussions.
Full contact but restricted martial arts also exist and mitigate risks by limiting the range of allowed techniques. Some of them do it in different ways than others. Judo is full-contact but disallows strikes, which makes it massively different than something with strikes. Semi-contact karate avoids the full-contact part, which makes it different in a different way.
Full contact practically always comes with risks, and full contact with fewer restrictions comes at much greater ones. Spectator expectations or other parts of culture may encourage the athletes to take risks and go to greater lengths than they otherwise would. But it's difficult for me to agree that modern society should have no place for sports that mentally healthy people actually want to participate in just because it comes with a risk of physical injury or intentional roughness. If they wanted to participate in a different sport, they'd have options.
In the end it's of course a matter of where to draw the line. Rather few people would nowadays want to allow fights to the death even if the participants wanted that. (Although, in reality, I don't think such a sport would get that many willing and actually voluntary participants either.)