FrogReaver
The most respectful and polite poster ever
I get where you are coming from and the framework is very closely aligned to how I view things. I don't like the term level there as I think players really establish what kind of hierarchy toward those types based on what they prefer and/or see as being less common.One reasonable conception of agency I've read divides it into three types, ranked lowest to highest (amount of agency). Here's a quick and dirty precis:
Agency Level 1: The freedom to deal with the situation. This is the an ogre jumps out of the birthday cake, what do you do? level of agency. Very common, and seldom quashed except by railroad tycoons.
Agency Level 2: The freedom to choose the situation. This is the level where players have the ability to choose their own route through an adventure. Whether that's multiple paths to pick from, or the freedom to creatively think of other approaches on the spot. Summed up, this is free exploration.
Agency Level 3: The freedom to choose the goal. This is sandbox agency, where the goals of play are player decided. They can do whatever they want. Rescue the princess, wash their hair, or go into business selling trinkets crafted by needy Goblin orphans.
What's interesting about this is that I see people talking about sandboxes and both levels 2 and 3 as the 'definitional agency' of that playstyle. I'm not suggesting that's wrong, only that different styles of sandbox involve different versions and complexions of the latter two. Most RPGs are pretty heavy on level 1 no matter what system or style. I wouldn't say this is by any means the last word in how to construe agency, but I do find it a helpful model.
Not to speak for people, but the impression I get from many is that "more agency" translates best to "more types of agency". Which is why I imagine that those explaining to me that my playstyle doesn't give players the agency to modify and introduce setting elements during play seems like such an important point. If you measure agency by the number of types present then showing me that my style doesn't contain all the types yours does is primae facie proof that my style has less agency. And if that's the measurement we are using for agency I would fully agree with that.
But no where has anyone defined what it actually means to have more agency. It's just a vague notion instead of even an attempt at a concrete definition.