It seems to me that the rules are the means by which players tend to exercise their agency on the game. Absent the rules, what let's them effect change? The most common answer is that the GM lets them do so. And if something I want is ultimately up to another to decide, it's hard to argue that I have a lot of agency in the situation.
I think that's what it boils down to.
And for clarity, by "rules" I don't just mean mechanics, but also processes and/or techniques of play.
I think your last line is crucial.
Consider three procedures for establishing the shared fiction - hitherto unestablished -
that there are hills to the north of the swamp:
* The PCs are in a swamp. One of them is a ranger with a favoured terrain (or similar) ability oriented towards hills. The player of that PC says,
I hope we can get out of this swamp into some hills. The GM responds,
Actually, your PC recalls that there are hills to the north of the swamp.
* The PCs are in a swamp. One of them is a ranger who is local to the area. The GM asks the player of that PC,
What is the land like to the north of the swamp? The player - who (for whatever reason) would like the action to move into hills - replies,
There are hills to the north of the swamp!
* The PCs are in swamp. One of them is a ranger who has an ability like Terrain-wise or Swamp-wise or Local landforms-wise. The player of that PC declares,
I'm pretty sure north of this swamp there are hills. The ability is tested, the check is a success, and the GM responds,
Yep, you're right to remember that north of the swamp there are hills.
Only the last involves resolution mechanics. I've described it using some Burning Wheel terminology, but Cortex+ Heroic would work similarly. And I'm sure there are other systems too that have this sort of procedure.
The second is borrowed from
@AbdulAlhazred, and is classic Dungeon World/Apocalypse World "ask questions and build on the answers". There is no resolution mechanic in play, but there is a clear process whereby the GM hands authority for establishing the shared fiction over to the player.
The first procedure is a very mild form of the GM taking suggestions. I could be wrong, but I don't think
@Crimson Longinus would have any particular issue with it. To me there seem to be two main differences between it and the DW/AW approach:
(1) A difference of principle: the GM isn't expected or obliged to take suggestions, and so the player's role is more tentative and more dependent on the GM's inclinations;
(2) A difference of process: the participants at the table may or may not be able to work out what has happened (ie the GM took a suggestion), but there is no overtness to it.
I tend to think that both (1) and (2) reduce the player agency compared to the DW/AW approach. But the player still had more agency than a circumstance in which the GM does not take suggestions at all.
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A variant of this that got a lot of discussion during the 4e era was players establishing "wish lists" of magic items for their PCs. I can think of 4 distinct procedures in this neighbourhood:
* The player mentions, in an unstructured/informal way,
It would be cool for my PC to have item XYZ. The GM notes this, and writes XYZ into his/her notes for some part of the map that the PCs are likely to come to soon.
* The player, in a formal way, presents the GM with a list of items s/he would like his/her PC to have. The GM notes this, and when an appropriate opportunity comes up to narrate a magic item into the fiction, the GM has regard to what's on the list.
* In play, the PCs arrive at a time and place where it would be appropriate to discover or receive a magic item. The GM asks the players,
What would you like it to be or some variant of that (eg
What do you see when you open the chest?) and so the players get to establish the narration at this point.
* In play, the PCs are in a context where it might make sense to discover an item. A player therefore declares,
I'm looking around for item XYZ. A check is made on an appropriate ability. If it succeeds, the player finds a XYZ.
The fourth of these is how BW or MHRP/Cortex+ Heroic works - in BW I've resolved this as a Scavenging check (both as player calling for the check, and as GM adjudicating it); in Cortex+ Heroic it's been an attempt to create an asset (tested against the Doom Pool). I've also done a version of this once or twice in 4e when obtaining or reforging an item was the outcome of a skill challenge.
The third of these is not an approach I've ever used, but I know that some 4e GMs (and maybe some other D&D GMs) have used it because I've read their posts.
The second is canonical 4e D&D (per the DMG) and is the main procedure I used when GMing that system. A lot of critics of 4e were critical of this procedure.
The first is, again, the weakest form of the GM taking suggestions. As with the parallel approach to
hills being north of the swamp, I assume that it would not be controversial with
@Crimson Longinus.
For my part, once you are accepting that a "good GM" will take suggestions in an informal or implicit or covert way (as per the first procedure in each of my lists), it seems to me that moving down the list is about taste and also about what do you want as part of your system design (eg the bottom approach on each list needs a way of setting difficulties for those tests - both BW and MHRP/Cortex+ Heroic have that, though it's quite different in each).
But I don't see any issue of deep principle - eg about who should be able to exercise what sort of authority over the shared fiction - that is implicated by moving down the list.