I think you're a little too attached to the idea that the example the discussion is revolving around is your own. I can't speak for Crimson, but when I evoke the example Im doing so on a theoretical or even hypothetical level; I'm using it to illustrate an issue.
What does it mean to invoke an example "hypothetically", without reference to (i) a RPG system, and (ii) a context of play.
I mean, which RPG do you take yourself to be "hypothetically" discussing, such that is suffers from an
illogical approach to the resolution of player rolls to find out if their characters succeed when using a skill?
we can change the example to "Aragorn stops to sharpen his sword, and the Nazgul show up". It doesn't make any difference to either Crimsons nor my arguments, but we no longer have to utilize your personal anecdote.
This drives home my points just above - what are you envisaging? I mean, if the scene is comparable to the one on Weathertop, with Nazgul known to be abroad, and Aragorn's player declares the action to try and get an edge and the action fails,
having the Nazgul choose that moment to assault the party looks like the right call (at least if the game is similar to Burning Wheel, Torchbearer, or HeroQuest revised).
What I deemed illogical was basing odds of things happening on stuff that would not causally affect them. Like
@Emberashh earlier explained, the procedure jumbles together several unrelated things. Now it is perfectly valid that one might want to make such a trade off for expedient game play, but lets not pretend that it is not a trade off and the logic of task resolution odds doesn't get messed up in the process.
I repeat that the meaning of "illogical" is not
contrary to @Crimson Longinus's preferences.
What the resolution system does is determine
whether the player (and their character) achieve what they want by using the skill in question. And having a higher skill makes the answer to this more likely to be
yes. That's not illogical - it poses and answers a completely coherent question via a completely clear process.
It's not a process of task resolution - if by "task resolution" is meant
finding out the degree of skill that the character displays in their efforts - but that doesn't make it incoherent or illogical. The rulebook is not confused or misleading on this point.
jumbling things together simply leads to disconnect of cause and effect, and creates weird decision logic. For example, "let's make chocolate chip cookies, not macarons, as latter are harder to make and we don't want to be attacked by the bandits."
So if you play a non-task resolution game and describe all your actions in terms of task resolution, the game won't work. But any such jumbling would be yours, not the game's. (And by that measure 5e D&D is illogical, because I narrate every hit as chopping of an opponent's limbs and eviscerating them, yet they don't fall down and keep moving at full speed!)
Anyway, I can tell you what the players in my Torchbearer game actually do: they consider, as their characters, how hard to push themselves, knowing that the harder the task attempted, the less likely they are to achieve what they want. The decision logic it creates is one that is salient to risk, threat and the demands of the situation. Which seems fitting for a game (Torchbearer 2e) whose tagline is
a roleplaying game of desperate adventure.