Everyone dances around this point and is vague.
If the player suggests anything and the DM has no veto, then it's forcing the DM to do something...even if the DM is a "fan of the players" and just agrees to do so "right away player whatever you say".
It's exactly like a DM saying "your character must get mad and chase after the gnome", but the player then saying "no, my character will just let it go". No player would want to "ok, my character chases the gnome and is mad because the DM told me to".
And if the player can't suggest, change, alter or create anything....then what exactly are they doing? Just decorations?
Even a "good" player might "suggest" a ton of stuff the DM does not want in the world. So, does the DM just roll over to the players automatically or can they say "no" or "well, not exactly like you said".
And IF they can....they CAN do it EVERY time a player suggested something. Right?
And if the DM can't say "no"...what is the control for the exploitive players or worse? When a player just says "oh...snicker, snicker, the temple of Good is selling healing potions half of today". Does the DM just roll over and say "Wow, cool idea...your wish is so in the game player." ?
I simply don't know of any RPG in existence in which Players simply get to state ANY ARBITRARY THING and have it simply appear as part of the fiction. I can't say there is no such RPG, there's a lot of them I have never experienced, but if so it must be structured completely differently than your trad conceptualization that is underpinning all your statements.
Lets go with an example of a narrativist RPG, Dungeon World, which I know very well. In DW players have no ability to state fiction AT ALL, aside from declarations of the actions of their PC, which must be consistent with the existing fiction. Given that these are 'low myth' games where the current situation/setting may not be fully fleshed out, its often true that players do make tentative assertions. Like in a bar fight a player might say, I run up the stairs onto the balcony and leap down on the big bruiser! OK, there wasn't a staircase or balcony specifically mentioned, but the GM is pretty likely to simply say something like "OK, sounds like Defy Danger CON!"
The GM in DW is NOT a "fan of the players" at all. She's a fan of the CHARACTERS. This is completely different! She's bound to want to see them put in dangerous fantastical situations where they can try cool things. Danger cannot exist where there's no possibility of harm, so harm must be on the table (at least in some situations). In fact "Inflict Harm" is literally a GM move in DW, a hard one, but lets say given the above action declaration for the PC a perfectly appropriate one, potentially (maybe if he fails his DD check).
Now, there is also a formal mechanism for a player to introduce some fiction, its called "Ask Questions, use the Answers" and its a GM thing! So, the GM might ask a player "Is there a shop in town which has what you want?" Why not? I mean, sure, the player is likely to answer 'yes', but that's not a given. Or maybe a better GM question might be "who runs the shop which has what you want?" OK, the player may answer that its his PC's friend, but now I can guarantee that friend is going to need his buddy before too long! There's no free lunch! Nor does the GM in a DW game have to simply accept an answer, he could tell you how the guy got robbed blind last night and you're going to have to go track down the thieves to get what you're after.
The game CENTERS ON the characters, it isn't a free ride for them! In fact quite the opposite, they're almost sure to be constantly in a pickle.