There are a lot of good thoughts in this post. I am intrigued by the idea, if I may rephrase, that "RPGs cannot replicate experiences which are primarily about vertigo". (I like the term vertigo because it fits into Caillois' classification).
Oh this whole post is worth it just for the Caillois' classification terminology, which I've somehow managed to avoid in all my study of games and sent me down a rabbit hole.
I disagree with Caillois fundamentally on certain points, but it's still worthwhile reading. Notably, I'd think if he'd realized the falsehood of "Games are not ruled and make-believe. Rather, they are ruled or make-believe." he would have been able to invent the modern RPG, but I think at the time he made his observation it was largely true that games fit into his either/or classification so I can see why he would have thought it.
So, a successful game that models mountain climbing has to focus on the aspects other than vertigo...and there are not many. That argument seems right to me.
My terminology (which I outline here:
Towards a Functional Taxonomy of Role-Playing Gamers) would map Cailois' Vertigo/Ilinx to a subset of Sensation. And yes, I think the part of Sensation that Caillois homes in on with Vertigo is very hard to do in an RPG, although I have achieved it a few times with children whose imaginations work more powerfully on them than adults who self-regulate against the sort of distortions of perception that would count as Ilinx.
However, it's worth noting that I think rather little of his other divisions, and in particular his mimicry concept is too vague, covering things that I can consider Sensation (the pleasure of imaging a sensation), Fantasy, Narrative, Expression, and Discovery.
I wonder how Callois would classify making a sand castle. Is it not play? Does he toss it into mimicry and just have done?
But, a successful expedition game has more to go on. There is strategy (do I press on through the storm or take shelter?), there is chance (will I discover a large waterfall here?) there can be competition (will we reach the goal before our opponents?). I think you have to emphasize those rather than experience of being a climber.
The above is a big part of my point. I don't particularly care for Callois distinctions, and I note that Richard Garfield's essay on chance (that I admire greatly) would contradict Callois' instincts here to say Chess has an element of chance in that in practice people play semi-randomly and so stumble into lines of play and in theory by doing so even an amateur might defeat a Grandmaster by pure luck. I don't count "chance" as element of why we play so much as I count as necessary for something I do agree with Callois on - that the outcome of play is not fixed. As Captain Sisko says, we love baseball because it is linear and we don't know what is going to happen.
But I do agree that we can focus on what we can bring to the table to make an expedition fun whether Challenge, Discovery, Narrative, or what have you. Imagine an adventure based on John Wayne's "The Cowboys" with the PC's in the roles of the inexperienced cow pokes learning the trail. This is straight forward traditional RPG play with some of the logistics abstracted out (because it's in the hands of an NPC and thus the GMs problem) and look at all the aesthetics we can meet.
The early part of "Skull & Shackles" has a great little minigame of sailing the ship as crew where a lot of the minigame is not letting the sailing grind you down, and it is pretty wonderful for making life about the ship feel unpleasant and dangerous. Something like that can be easily adapted to something like riding with the herd on the trail with an early "Can you keep the cows alive?" focus. Depending on the system (BRP) you could even finish each day with a skill test to determine whether you learned something on the day and did a mini "level up".
Advantage/disadvantage is also pretty recent. Although maybe that is less of a fundamental shift.
Bloodbowl (1987) has a mechanic where if you are at advantage you take the best of two dice, but if you are disadvantage your opponent chooses the result of two dice (whatever they think is your worst result presumably). Over the Edge (1992) used a very similar mechanic of granting advantage by adding an extra dice to 2D6 and taking the best two of three or granting disadvantage by adding an extra dice and taking the worst two of three. It starts showing up in 3e D&D as rerolls where you can take the better of two results and gradually becomes more pervasive. For example, prior to the publication of 4E I already had in 3e a Skill Mastery feat, that when making a skill check you did so by rolling two dice and taking the best result. Later editions just make it generic, for better or worse (I'm mostly inclined to think for worse).
I would welcome disagreement. My thoughts are only half baked on these questions.
Baking my own thoughts are what a lot of my long posts are about. So I very much welcome the disagreement, feedback, and discussion.