These are all propositions that only have meaning within a shared fiction. If those are the sorts of goals you're interested, I don't understand how you can deny the centrality of shared, negotiated imagination. Unless the other participants in the game somehow become obliged to imagine (say) that Nation X has declared war, how can you achieve your goal of having X tricked into declaring war?
Until we talk about what power the GM has, and how (if at all) that might be constrained, we can't know anything about the connection between player action declarations and achieving the goals you describe.
Will climbing the mountain help with lighting the signal fire? Not if there is a giant at the top who eats all climbers; or if there is a portal to the Plane of Ice which makes lighting fires impossible; or if the character loses all their fuel, tinder etc during the climb.
So now we're back to "can a person reasonably simulate a fictional world in their head, and tell you about it when asked?"
Which frankly, I'm just willing to take as a given, because you can't get any of that juicy gameplay otherwise, and I've yet to see a better technology for doing it. Other mediums have sharply more limited axes of interaction.
It is significantly different to decide there is an ancient signal beacon guarded by giants, and to decide there is an ancient signal flare guarded by giants in response to a climb check. The former presents a board state a player can make meaningful decisions about, and the latter does not.
There are RPGs with mechanics that govern these sorts of things, including DW, Torchbearer, Burning Wheel, and 4e's skill challenges.
But you seem to be talking about RPGs with mechanics more like 3E D&D or RQ or RM, which do not govern the sorts of things I've mentioned. Which means that the mechanics do not mediate the utility of abilities for achieving goals.
That's quite a bold take. Jumping from "building a fictional setting and simulating all the non-PC members is Player Y's responsibility" to "therefor, Player Y decides the outcomes of all actions" does not follow for anything but the most skewed take on that relationship. Once you've created a setting, you don't need to make any more decisions about it, you can just let the players declare actions and let the game resolve them.
As far as telling that the goal has been achieved, in the sort of play you are advocating I understand that only the GM can do that. So the mechanics that govern the GM in this respect seem pretty important. Probably more important than the rules for skill check DCs!
There's an interesting design question there. The gameplay loop I'm looking for requires the board state's changing in response to a player's actions be entirely mechanically mediated. If the player is to have the ability to more or less efficiently navigate to a victory condition, then the board has to exist in a knowable state the whole time and the effect of each action has to be known.
Within those constraints, I don't see a problem with setting rules on the GM's worldbuilding, you'd just need to do it before play began. You'd end up with something like a particularly proscriptive setting/dungeon building guidebook.
I don't know who you're attributing this assumption to. It doesn't apply in any RPG I play. To my mind, the bolded bit is a necessary assumption for skilled play in the Gygaxian mould. To render it unnecessary requires significant departures from Gygax's play procedures.
I was presenting it as an absurdity, that assigning all responsibility for fictional results to the GM would necessitate.
My model would offload that interaction to the rules. They should be able to tell me the results of any action I declare (within reason, eventually you're likely to run into an unavoidable edge case, but the frequency with which it occurs in heroic fantasy is routinely overstated). I expect a GM to determine, for example, that a wall is made of stone, for any of number of reasons; naturalism, extrapolation from an established setting, because they recently read an article about quarrying procedures in antiquity, it doesn't honestly matter.
That the wall is made of stone then creates a vast network of game information about that wall, some of which the DM may even have had in mind, and much of which I don't expect them to have given much thought. The climb DC of an unworked stone wall is X, the hardness of stone is Y/inch (which produces the derived statistic "time to break wall with an adamantine dagger is Z), the spells Meld with Stone, Stoneshape, Transmute Stone to Flesh all have interactions unlocked, goliaths and dwarves new perception/combat actions available, the necessary strength to remove stone quarried with that adamantine dagger is Q and on and on and on.
The decision produces a pretty astounding amount of points of interaction, and the GM should not (and probably can't) consider all of them before determining the nature of the wall, but the process for resolving any of them will not involve the GM making a decision after that.
With only a little cheating on causality (did I know the precise thickness of that wall, before the players pulled out that adamantine dagger? No, but I can simulate the state I was in when I decided the wall was stone, step back to worldbuilding mode for a moment and figure it out) a GM can create a board state that will yield a bunch of different outcomes, of variable values in response to a bunch of different declared player actions. There are lines of play to interact with this wall that might be better, or worse, and players will pick something. Probably just walking past the wall.
D&D conflict is not task resolution - it's conflict resolution. (With hit points as the "clock".) And it is intent-based resolution: the depletion of hit points does not just represent "Your struck the elemental with your sword" but "You have pushed the elemental this much closer to your goal of its demise".
It's possible to have an analogue to D&D combat for climbing a mountain to light a signal fire. 4e skill challenges are one model. But there are plenty of others too. The only one that I know of, in the space of RPGs that you seem to favour, is Rolemaster with its manoeuvre tables (though it's a bit "proto" in character - it will get you to the top of the mountain, but the GM is still at liberty to have a giant there who eats you!).
I honestly have no idea how this has anything to do with the point I was making, and don't know how to respond to it.
The important thing I'm trying to convey is that there are multiple lines of play between the living elemental trying to kill you and the dead elemental the player wants, and that their decisions can be better or worse in getting from point A to point B, increasing or decreasing the likelihood they get there. Combat is a poor example, because it's part of the game that forces you to engage in gambling and has a generally pretty binary board state and victory condition without bringing in morale rules, but I went with it because we all more or less understand the optimization case it presents.