Apparently rugby (the OG version of American football where people don’t dress like sofas) is actually safer than the American one because the lack of padding means they’re less likely to do anything stupid. Kinda like how boxing became a more deadly sport when the rules were finalised and they made people wear padded boxing gloves because it meant you could really brain somebody without breaking every bone in your hand in the process, which is what used to happen in bare-knuckle prizefighting.
“Dermatologists HATE him!”
With rugby it is more that the serious head injuries are not common.
Mainly because the rules don't call for headlong charges into each other, instead they tackle around the legs or waist, and form a scrum, in which they lock arms over shoulders and push each other, while the ball is kicked back out of the scrum.
Rugby players do often suffer smashed teeth, knee issues, bites in the back of the head, torn ears, and if they belong to a particularly boisterous club, alcohol poisoning, hypothermia from wearing nothing but a thin flowery dress and a pair of plastic tits, plus rectal prolapse when they pass out face first and have bottles put in their bottoms.
Or they play the other sort of rugby which is more like what you call "Touch Football" so it minces into Soccer football territory, as in a game for jesses, poofs and big girls blouses as they skip and prance around a field chasing each other.
Boxing, yes the gloves turned it into a sport with a lot more knockouts and the like, as bare knuckle fighters rarely punched to the head with a closed hand, for the reasons you say. Open handed slaps and heel of the hand punches were more common to the head and face, with a closed fist used on the torso as it was more forgiving on the hands.
Matches would go on for hours, rather than minutes. This was one of the reasons they thought it would be better to have gloves and standard rules.
Many people these days would agree that the demise of rugby as a sport for boys has caused this plague of troonery as many believe it knocks the Fancy foo foos right out of them.