Reductio ad absurdum has the tendency of backfiring when you look more like you are trying to be difficult than you are trying to get at something substantive. Wriggling your way into a corner case of absolute logic that a casual discussion didn't deal with explicitly does not mean the opponent needs to throw their hands in the air and accept you are correct.
Which is to say - in a discussion of good faith, trying to be reasonable is preferable to 'gotchas'. Leave room for colloquial use of language, please and thanks.
Where I was going with it (before I got distracted and forgot to get back to it) was that I could see someone deciding to use Cha for a climbing check if it was described right and this is due to using the right ability for what is being described as the stakes.
So the characters are going up the mountain. If the goal is to get to the top - climbing check.
If the goal is to get to the top without losing an important item (getting to the top is not in question) - survival check (packing skills).
If the goal it to get to the top quickly before your objective gets beyond your grasp - so they decide to hire a guide (getting to the top is not in question, just time). The quality of the guide you track down and persuade to take you is the thing that is being checked (Cha)Persuasion, modified by local contacts etc.
The point was that Cha could be a valid thing to roll for a climb check if it matched what was at risk for failure of the roll.
For me matching the ability to the outcome or results of the action is far more important than to matching it to the action being done.
For example: if the characters are crossing a river and the DM decides that a failed swim roll Str(Athletics) results in being attacked by a crocodile.
The disconnect of failure to swim = attacked I find irritating.
If there is a chance that anyone swimming might be attacked by a crocodile, then someone who is stronger shouldn't have less chance of being attacked by the crocodile.
However a survival roll before going would alert them to the danger, and they might choose a different course of action.
What I could see in this situation would be a failed swim roll causes you to be in the water for longer. increasing the chance of being attacked.
Those who make their swim check are attacked on 1-2 on a d20. those who failed will be attacked on a 1-4.
While the difference is subtle in the first example the failed swim "causes" the crocodile to attack. In the second the swim check means they are in the water longer thus increasing the danger.
It is a similar situation when someone is picking a lock and the "fail forward" it that they open the lock but a wandering monster comes along. I am much happier with it taking a long time and so more checks for wandering monsters are made, as the failed roll result in it taking longer, not in making a monster appear.
It wasn't trying to gottcha anyone, I was trying to show that different people need different levels of connectedness between the rolls being made and the results in generates. I like a high level of connectedness, other like less. Neither is wrong (just preference).