For this tangent I’m going to be speaking under the assumption that different games have differing amounts of agency.
1) Particular game rules make for different games
2) particular game rules make for differing amounts of agency
Thus, To the game rules is to change both the game and the agency it offers.
This next piece I think is why @clearstream has been working towards. Given that all games limit agency to some degree in order to be a game - then there should be games with more agency than PbtA or burning wheel or etc (and if they don’t currently exist then they theoretically do so as we can all imagine them). In short the posters saying they prefer higher agency games aren’t actually looking for the highest agency possible. Instead they are content with the amount and types PbtA and others offer them. It’s not simply a desire for high agency - it’s also a desire for particular types of game rules.
What this and the points above together show - agency and game rules are inseparable. To be content with a certain level of agency is to be content with the rules of that game and to be content with the rules of a game means you are content with the level and types of agency it provides. This conception of agency in relation to playing games is a tautology - and that’s is trying to be conveyed.
But you still have the players and (in most systems, in particular) the GM using the system, which does change the "baseline" of the system. For example, a GM can deprive players of agency in any kind of system by making a certain type of scenario. This can be done even purely using prepared materials and no direct railroading. You can devise sandboxes that regardless of how impartially you adjudicate the game, the players have low agency when acting within them. And the opposite holds too - a system which is comparatively low agency can be turned into a session of massive agency if the GM hosts a session that gives players tons of agency by virtue of the scenario and the interactions.
That doesn't mean I think agency is irrelevant and everything is the same. I'm saying that the system is part of what contributes to agency (and it can be a big part) - but one cannot ignore the people playing the game. I'm pretty sure there are posters in this thread who would GM a "vanilla" 5th edition game so radically different that the player agency was as different, as if they were using different systems.
So yes, agency and game rules are inseparable. But agency and conventions, preparation style and scenario conditions are also inseparable. Which makes sense - all aspects of the game (system and human) contribute to the type and level of player agency.
I don't think agency when it comes to negotiating (explicitly or implicitly) the social contract for a game is an unimportant and not real agency. Especially as the negotiation in practice may often not be purely a session 0 thing. While some are lucky to have groups where the expectations are known and aligned ahead of time - there are many tables where the contract is constantly being renegotiated in various minor ways. "Can I do this?" "Could we do this?" "I'd really you rather didn't do this." and so forth. In such groups, a player who is left without ability to properly affect this process can feel loss of agency.
Are any of these (hypothetical) examples of lacking of agency less valid?
- we're playing D&D and it doesn't let me do what PtbA does in regard to the shared fiction
- the GM is using quantum ogres all the time and my choices are fake
- the group is constantly shutting down my attempts at shifting the game towards urban adventures and social interactions instead of hack 'n slash dungeon crawls?
- the GM has prepared an obnoxiously difficult scenario and it's really hard not to be forced into a game of stealth, resource management and min/max'ing of mechanics - which I might not find interesting
- the other players are spending half the game session chatting up NPCs, but I'm playing a mute cyborg and I just want to get to some proper combat and action adventures
I agree that system is an important factor, but there are so many aspects contributing to player agency that I think it is important to consider it as a multi-dimensional and complex concept, highly tied to what the player is actually trying achieve by playing the game.