1. http://ejmas.com/jcs/jcsart_svinth_a_0700.htm
2. https://www.nsaa.org/media/68045/NSAA-Facts-About-Skiing-Sno...
You could very easily get hurt more in a minute of boxing than in a lifetime of skiing. It seems crazy to me too to state that the former is less dangerous than the latter. The statistics bear it out, too.
I think you're right about injury rates of skiing vs boxing, but I don't find your anecdote convincing. One could just as easily say, "I've been free-solo rock climbing for a decade and I've never gotten more than a blister." Different sports have different distributions of injuries. In some, you're perfectly fine until you're dead. In others, you slowly accumulate damage. Because of this, it's better to ignore anecdotes (even ones involving lifetime experience) and look at stats.
FORCE = MASS X ACCELERATION.
The extra mass is something the skull and brain cannot take. Also, the protection of the weapon (hands) assures fights go on linger than in bare knucke boxing. There is conflicting evidence however.
I suspect bare knuckle boxing is less satisfying (and thus less popular) because fights can end merely because one person can no longer effectively attack, rather than when one person is conclusively defeated by being knocked out. The KO is always the most widely satisfying finish in boxing and MMA.
Actually...
http://www.latimes.com/science/sciencenow/la-sci-sn-human-fi...
Bare-knuckle fights can go on for a long, long time. I can't find the source just now, but I recall some fights went on for up to 24 hours.
That doesn't televise well.
Gloves allow head blows. Now the human body's ability to take blunt force damage is very high, when not hitting the balls or the head. So you get longer and not as spectacular fights.
Same with professional football compared to rugby of old. (although it seems rugby after 90s have similar problems after the sport tried to become more spectacular).
As I understand it (boxing's not my martial art of choice but I know a bit about it), boxers spend most of their time training, not fighting competitively. Per year, you might well find a professional skiier spends more days skiing than a professional boxer spends minutes in the ring.
See https://www.reddit.com/r/Boxing/comments/24r83s/how_many_fig...
I am, of course, assuming that professional skiiers ski a lot, but that seems like a reasonable assumption :)