There are countless counter-examples to this claim. For example, Jerzy Kukuczka's spent three nights out above 8000m on K2 without food, water, tent, or sleeping bag. During this time, he covered substantial technical ground to summit their new route (the South Face) and descended safely without assistance and even without frostbite. His partner, Tadeusz Piotrowski, was suffering more seriously from the exposure and fell while downclimbing ice unroped. Kukuczka was not just "lucky", he was prepared and knew how to last in extreme conditions. His decision-making with regard to batteries (his headlamp never worked when it mattered) and rope (he died when the second-hand 6mm rope he was leading on cut) was not so good.
Touching the Void is a great story and Joe Simpson is an entertaining writer, but he's also notoriously accident-prone and has some peculiar risk analysis judging from his writing about places that I have climbed. Sure, cutting edge alpine-style climbing is dangerous and requires a great deal of competence, but it's still not crazy gamble you describe as long as you make objective decisions.
I have tremendous respect for the abilities of the climbers, they are obviously among the best in the world in several categories of physical prowess, but it still seems that mountain climbing is one of very few disciplines where you can do everything right and still, with a reasonable probability, get killed due to some random circumstance.
There are a lot of decisions that affect the risk level. This is the same with any activity. Cutting edge climbs generally involve enough "risky" decisions to be considered dangerous, I have lost too many friends to claim otherwise. But there is a lot of "serious looking" climbing, including quite a lot at high altitude as well as very technical routes that can be done at a risk level similar to non-"extreme" activities.
Accidents on hard routes are either because of objective hazard (e.g. climbing underneath a serac, an obvious hazard that the climbers chose to accept because they thought the route was "worth it") or human error (e.g. rappelling accident). You choose where to climb and you assess conditions. Some hazards are hard to assess (avalanches from slopes that you cannot evaluate), but most accidents related to objective hazard involve a specific decision that was known by the participants to be risky.
It is not the case that choosing to attempt a big objective involves an especially large risk. But if you never make risky decisions, then you are likely to fail at your objective (maybe climb something less impressive). The trick the prolific climbers who make it to old age have mastered is evaluating risk sufficiently accurately to get the big lines without dying. There are a couple who were just lucky, but by and large, luck runs out eventually so you have to be good at assessing risk.
If you play games where one set of moves means you'll certainly survive and win, then you're going to make those moves. It's like playing chess, with a loaded gun beside the board so you could shoot yourself if you chose to. That might give you a thrill the first time, but you'd soon get bored of it, and you wouldn't learn anything worthwhile from it.
The really absorbing games are the ones where every set of moves could get you killed, and the winning ones are more likely to than the safest losing ones.
Many books have been written about this stuff. I think Joe Simpson's This Game of Ghosts is the most accessible.
That's not really a counterexample, at least not to the claim you're disagreeing with. He was not just lucky, but he was nonetheless quite lucky. If apparently solid ground had just given way under Jerzy Kukuczka or the terrain above him had come crashing down on his head, or the temperature had suddenly dropped a lot further, he still would have died, wouldn't he?
The lower part of that route was quite dangerous in terms of rock and ice fall, but that was mostly behind them once they reached the upper part. Crevasses don't just occur anywhere, and they were mostly on technical ground where it was a non-issue. Ridges can have cornices, but if you are paying attention, you can usually find a way to traverse the ridge in a safe place (this might be much slower/harder). Usually you use a rope on serious cornice terrain and you carefully choose how to run it so that it offers some safety, but big falls are definitely possible. They didn't have serious cornices on that route.
I do believe that Jerzy lived through that event due to his preparation/talent for handling extreme conditions and his mental focus (to keep warm when sitting in the snow all night, to not make mistakes after being out for so long). Piotrowski was no slouch, but he fell because he got sloppy. Perhaps his physiology was also somehow less robust. Note that lots of other people have died because of one night out in the same conditions, even following a comfortable tent-bound night of sleep and a day with food and water. These two were strung out from their big new route and after the second night of sitting in the snow shivering without food or water, they still broke trail up to the summit. It was after the third night out that Piotrowski finally got sloppy on the ice climbing.
There are countless counter-examples to this claim. For example, Jerzy Kukuczka's spent three nights out above 8000m on K2 without food, water, tent, or sleeping bag. During this time, he covered substantial technical ground to summit their new route (the South Face) and descended safely without assistance and even without frostbite. His partner, Tadeusz Piotrowski, was suffering more seriously from the exposure and fell while downclimbing ice unroped. Kukuczka was not just "lucky", he was prepared and knew how to last in extreme conditions. His decision-making with regard to batteries (his headlamp never worked when it mattered) and rope (he died when the second-hand 6mm rope he was leading on cut) was not so good.
Touching the Void is a great story and Joe Simpson is an entertaining writer, but he's also notoriously accident-prone and has some peculiar risk analysis judging from his writing about places that I have climbed. Sure, cutting edge alpine-style climbing is dangerous and requires a great deal of competence, but it's still not crazy gamble you describe as long as you make objective decisions.