When the details of the fictional space no longer have any bearing on the resolution of actions that involve interacting with it then yes it HAS become irrelevant.
OK, but that's different from what I said. For example, those details can be - and in many systems often are - relevant to determining the difficulty of a check. In both B/X D&D and in AD&D, for example, the likelihood of a pursuing monster giving up the chase is influenced by the dropping of food and/or treasure. The fact that the evasion check is, in the last analysis, boiled down to a die roll doesn't mean that the fiction didn't matter. In that sort of game, for example, dropping rations shouldn't
just be a mechanical matter of changing an entry on a character sheet (although it will involve such a change). In an exploration-oriented game of that sort it should also affect the fictional situation of the PC.
You are somewhat incorrect about old school D&D task resolution. While a stat check or a random roll can be used to determine an outcome, it is also possible to get a successful outcome simply by picking up on clues from the environment and acting on them. The dice are there to determine outcomes when the situation is in doubt.
Take another look at the example of play from the 1E DMG. The part where the party is exploring the room with the stream and the mineral formations. I don't see any reference to dice being rolled for the player inquiring about the mineral formations. The player explored the gameworld and made a discovery via that interaction.
That is true, but seems orthogonal to Hussar's post and your response.
In Unearthed Arcana, jump distances for thief acrobats are listed in feet, as I recall, but for barbarians are listed as a range of feet, presumably to be resolved via die roll (at least in some cases). The player of a barbarian whose PC comes to a pit can first try and judge it's width (many GMs allows this information to be known automatically), and then work out the likelihood of a successful jump. This doesn't mean that the fiction has become irrelevant to the action resolution. It has framed the parameters of the die roll required.
A thief climbing a wall is similar. I am prepared to assert that only a tiny fraction of wall climbs in AD&D games have been resolved not by die roll, but by the GM describing the holds on the surface and the player of the thief describing how his/her PC traverses those holds.
DM: "This room was once a barracks, you see smashed bunk beds and footlockers strewn about the room, in the......"
Player: " Yeah yeah, we search everything and take 20. What do we find?"
I have a personal view on how such mechanics should be analysed.
They are not action resolution mechanics at all. They are scene-revising mechanics. By calling for the skill check, in effect what the player is doing is saying "I don't like the scene in which I don't know what's in this room. I want to roll a die, and if I win then I want you to reframe the scene as one in which I see the concealed things in the room."
I don't have a strong view on whether it is good or bad to include such mechanics in the game, but I think the starting point for answering that question is to properly understand what their function is.
These days if player were not allowed to find that cylinder with a good enough die check there would be cries of foul play. Engaging with the game world (known in some circles as playing the game) is called pixel bitching now.
The game has steadily morphed from exploring the environment to a gauntlet of dice rolling probability challenges.
My reading of it is a bit different. Players still (apparently) want the tropes of being dungeon explorers, but actually playing through the game of dungeon exploration bores them silly. Therefore they like reframing mechanics like Perception checks.
3E's social mechanics are, I think, best analysed the same way. A Diplomacy check isn't action resolution; it's a chance for the player to have the scene reframed as one in which an opposed or unhelpful NPC instead is a friendly and helpful NPC. (I suspect the motivation for this is partly that roleplaying interaction is seen by some players as boring, and partly because many players don't like freeform roleplaying of interaction encounters and so, having no familiarity with decent mechanics for handling such things, opt for the "scene-rewriting" mechanics instead.)
I think the prospects of large numbers of players suddenly becoming enthusiastic for exploring streams looking for cylinders are dim. I also think the prospects of getting decent social encounter resolution mechanics from the D&Dnext project are dim. I therefore suspect that the mechancis that irritate you are likely to remain - if they're not printed as official rules, the players who rely upon them as scene-framing tools will have to reintroduce them!
But anyway, all of that is (in my view) quite orthogonal to the question of whether dice-based action resolution mechanics undermine the place of the fiction. C&S, RQ, GURPS, RM, Traveller, etc - nearly all the games of the first post-D&D generation - have extensive mechanical systems based on (i) identify the fictional obstacle to be overcome, (ii) determine the die roll required, (iii) make the die roll, (iv) extrapolate back to the fiction. And to the best of my knowledge it's never been suggested that those mechanics undermine the character of those games as RPGs in which the players play the game by engaging with the gameworld.