It's not really that. It is merely that for choices to matter there must be some constraints and limiting the players ability to affect the setting to that of their character is one possible constraint.
Here's one way to limit what the players can do in a RPG: all they do is listen to what the GM tells them is happening, but they elaborate on it a bit with (what @Manberacat, not far upthread, called) characterisation/pantomiming.
Such RPGing actually takes place. I've seen it. I've read posts about it. I've participated in it.
Those limits don't make choices by players matter. They make choices by players, beyond the zone of characterisation/pantomiming, largely irrelevant.
The main "limit" that makes choices matter in a puzzle-solving RPG is that
there is a correct answer to the puzzle.
The main "limit" that makes choices matter in "play to find out what happens"-type RPGing is that
what happens can't just be ignored.
People seem to recognise this in a sense that they accept that the game needs to have rules; that a situation where the players can just freely declare anything and have it be so is not optimal. I really want people to answer this: do rules that place limits on how the player can affect the fiction or 'gamestates' reduce the players agency? And if they do, why we have such rules?
These questions, in so far as they apply to "play to find out what happens"-type RPGing, have been amply answered upthread.
In games that use "say 'yes' or roll the dice" - eg Burning Wheel - the point of resolution mechanics (ie "rolling the dice") is to find out who gets to say what happens next - player or GM - and to determine the constraints that govern that - will it be the player's desire for what happens to his/her PC that comes true (ie if the GM says "yes", or if a roll is a success) or will it be some sort of adversity for the PC narrated by the GM (ie a roll is a failure).
In PbtA games like Apocalypse World or Dungeon World, the point of resolution mechanics is to find out, at certain key moments, who gets to say what happens next. The system determines what counts as a "key moment" by its list of player-side "moves" (the slogan is,
if you do it, you do it; if a group discovers that the systems list of moves doesn't correspond to what they care about in play, then they're playing the wrong game and should find one better suited to their tastes). If a move is triggered then we work out who gets to decided what happens next by rolling the dice - on a 6- result the GM gets to say what happens next, and is allowed to go hard in that respect; on a 10+ the player generally gets quite a bit of say over what happens next or perhaps (eg in AW if Go Aggro is used against a NPC) the GM gets to say but is significant constrained; on a 7-9 maybe the player gets to say but is significantly constrained (eg Seize by Force in AW) or maybe the GM and player get to share it a bit (eg Do Something Under Fire in AW).
In AW, there are very few player-side moves that permit the player to establish what it is that his/her PC knows, sees or recalls. Here's an exception, from the Batlebabe:
Visions of death: when you go into battle, roll+weird. On a 10+, name one person who’ll die and one who’ll live. On a 7–9, name one person who’ll die OR one person who’ll live. Don’t name a player’s character; name NPCs only. The MC will make your vision come true, if it’s even remotely possible. On a miss, you foresee your own death, and accordingly take -1 throughout the battle.
Generally, though, when a player wants to establish what it is that his/her PC knows, sees or recalls this is done via moves that (on a success) oblige the GM to narrate certain things under various sorts of constraints, including (if the player's roll is a success) that the information be relevant or useful (eg Read a Charged Situation; Read a Person; Open Your Mind to the World's Psychic Maelstrom). The GM is also directed by the game rules to
ask provocative questions [of the players] and build on the answers [that they give]. This (or, rather, it's Dungeon World equivalent) is the principle that
@AbdulAlhazred had in mind upthread when envisaging that a player might be asked
what landform is to the north of the swamp?
Burning Wheel takes a different approach to establishing what it is that his/her PC knows, sees or recalls. The player is typically permitted to put this to the test, via action declaration. Because such actions have a chance of failure, they open up the possibility that what it the PC knows, see or recalls either (i) isn't what the player hoped for, or (ii) isn't going to be as useful as the player had hoped. (Eg
Don't I recall that there are hills to the north of this swamp? OK, test Travel-wise. <Player rolls and fails> Yes, you do; you also recall that the hills are cursed - no one who has entered them has ever left alive!)
What makes all of this
matter is that the fiction
is what it is. Once established, it's established. If you're not sure about why this would matter, review the play example upthread of Thurgon and Aramina's encounter with Rufus. Or of their subsequent encounter with Xanthippe.
Yes, such rules may result in less agency for players than the rules of another game may allow. As to why would we have them, it’ll vary from person to person according to preference, but the general answer is that the rules result in an engaging play experience.
And then you also have an answer for why it might be desirable for GM to decide certain things instead of the player. But now you have basically agree that limiting player agency (as you define it) is often needed. So then this is really not about agency, it is about how that limiting happens.
Your post doesn't follow from the post you've quoted. By "such rules",
@hawkeyefan means rule for "things decided by GM fiat," And what is said about such rules is the fairly obvious point that
we would use such rules to produce an engaging play experience.
It doesn't remotely follow from that
all that matters in RPG design, with respect to player agency, is how such agency is limited.
The GM can be 'constrained' by their desire to make sure that everyone is having good time.
That's not a constraint. Which your scare quotes acknowledge.
The reason player's choices for their PCs
matter, in "play to find out what happens"-type RPGing, is that
everyone at the table cares about the fiction and those choices
help establish what that fiction is. What distinguishes this from cooperative, round-robin storytelling is that the set-up of the game means that (i) a certain group of participants (ie the players) have an especial stake in one or more protagonists, towards whom they adopt a first-person identification, and that (ii) all the decision-making about what happens next is oriented towards the fate of those protagonists based around what they try and do.
If you are playing RPGs as a type of puzzle-solving game then what makes the player's choices matter is that they can genuinely contribute to solving the puzzle. This generally depends upon the puzzle-maker not being able to change the parameters of the puzzle part-way through the attempt to solve it.
Neither of these approaches to RPGing generates any particular demand that the non-player participant (ie the GM) (a) be able to make up fiction during the course of play as s/he sees fit, nor (b) that there be strong limits on the topics of fiction that the players contribute.