I don't agree with this, because...
I don't agree with this. I think... I'm pretty sure I just don't see agency in the same way than you do. I try to explain. If you get to define both the conditions, and the reaction to those conditions; define both the question and the answer; then, yes, in a sense you have more freedom. But I wouldn't say that you necessarily have more agency. Agency, at least in the context of a game, is making meaningful choices, and I feel that it is the limits that make the choices meaningful. You respond to something external, and this makes your responses meaningful. If anything that limits the player's freedom is seen as reduction of agency, then ultimate agency would be achieved by removing the rules, the dice and the other players as all of those limit the player's freedom. And I'm not sure that this would be a reasonable or useful definition of agency.
The thing you're describing in the last paragraph has a name -- the Czege Principle -- which, as simply stated by it's author is, "When one person is the
author of both the character's adversity and its resolution, play isn't fun." This is well known in the design circles that the games we're talking about come from, and is avoided. So, your formulation isn't actually a thing that happens.
What does happen is that the players can narration an action -- something their character does -- and have that tested by the mechanics to see what happens. This includes things that establish fictional elements at times, but it's fundamentally about not having to ask permission to try the action before doing so.
It's somewhat informative to look at a situation where the players are looking for a macguffin, for whatever reason you wish to imagine. Through play, they find themselves in a room with a chest. A player declares their going to open the chest to see if the macguffin is inside. Here's were we can evaluate whether or not this involved more or less agency by way of approach. In the traditional sense, the player searching the chest can only ever discover what the GM decides (in their notes or in the moment) is in the chest. The act of search can discover information, but that information is determined by another player, by fiat. The GM has, at all times, the ultimate authority here, and can decide however they want what is in the chest regardless of the player's action declarations. There is agency here, but it's the agency to choose which parts of of the GM's choices you explore. Let's use my preferred assumption, here and in the next example, that everyone is playing in good faith so that we can avoid any diversions into Force or Illusionism or whatever. Functionally, the player can only ever discover that which the GM has decided.
In the second method, the GM has as much idea as to what's in the chest as the player, which is to say very little. The player has stated that they're searching the chest with the intent to find the macguffin. The GM, in this approach, can agree -- the macguffin is in the chest after all -- and should do so if this isn't a very interesting question. I think it is, and so the GM should challenge this action by submitting it to the mechanics of the system to determine what is in the chest. The dice roll, and determine who gets to say what -- if the player succeeds, the macguffin is in the chest and everyone at the table finds out this fact at the same time. If the player fails, then the macguffin is not in the chest or there's some other bad consequence -- perhaps, the chest is locked tightly with magic, and impossible to open without violence, so they'll have to do something more drastic to get it open which risks what's inside (ie, the GM threatens worse harm and extends the situation). Here, what is at stake is the player's intent, not just their action. This increases agency because the player now isn't just exploring someone else's ideas, but instead can add their own and see how they turn out.
Now, is the second way a better way to play because it has more agency? Absolutely not, or, more precisely, each person should answer that for themselves. My Blades in the Dark game, for instance, has way more agency than my 5e game, but I still run both because, while 5e has lower agency, it does have increased tactical minigames (char-op, combat, exploration, etc.) and I like those, too. All in all, over the last 2 years, at least 2/3rd of our gaming has been 5e, with Blades grabbing such a large share due to being easier to organize and run during the pandemic. So, more agency doesn't mean better, but it's hard to argue, without twisting into pretzels, that games that allow players more influence over the course of play don't feature more agency. They may feature less fun for your table, though, so, by all means, maximize fun! That's what should be the focus. Discussion of agency is a way to better understand how your game works and what alternatives exist, that's all.
And, for what it's worth, I was exactly in your shoes about 5-6 years ago. Like, I made your arguments to
@pemerton, and I thought he was a tad loony, too, what with all the obviously crazy talk about players getting to make things up. Can't say why, though, but something was said in one of these discussions that made me pause, and then I realized there's a fundamental perspective shift necessary. If you continue to evaluate these things with the lens of what you already know, you'll always be baffled by it. If you, instead, start by saying, "okay, let's assume this works, how does it do that," you can make the intuitive leap and see the other side. You might not like it --
@prabe has made a few steps and is a very worthy discussion partner, but he hasn't liked what he's seen so far, and that's fine -- great even. I'd be disappointed if everyone agreed with me -- why have an internet without discussion?