I'm not sure what you mean by "invalidate".
The player of the dummy hand in bridge obviously doesn't have agency, because their partner gets to play all their cards. The fact that it is their partner who is in control doesn't change their lack of agency.
Invalidate -- make pointless. I know OP has said RPGing isn't necessarily pointless even if they players have no agency. I guess I agree, but would argue that even playstyles requiring player agency work with trad GM power.
I don't know how to play bridge, but if the players have a conversation about what should be done with the dummy hand (as happens constantly between the GM and players in an RPG) they share control, unless one player has no capacity to influence the other.
When it comes to RPGing, if the GM is in control, then it seems clear enough that the players are not.
That's not clear to me. I can think of many situations where people share control over something, even when one person has the final say.
If I convince my boss at work that a project is worth doing, is that not an expression of agency because they had final say?
Does a film director not have any agency at all unless they have final cut?
What about sports like boxing, figure skating or gymnastics where the winner is decided by a judge? Are those sham competitions because to some degree the outcome is up to the judges' whim?
In each case I would say of course they have agency, assuming they have at least some influence over the judge.
Furthermore we can usually identify capricious or biased judges. So rules preventing them from acting this way aren't necessary. Same thing with GMs and RPGs. Players can tell when they don't have any influence over the game and tend to leave games like that. There are mechanisms to correct the problem on the meta-game level.
No, it absolutely is not. There are participants in a game. Those participants can have agency or not, according to inviolable rules, which the players know and rely on to achieve known goals.
The game can be competitive (chess) or collaborative (Pandemic, Too Many Bones) and these structural components of agency remain the same.
If your point is that RPGs can be perfectly functional and enjoyable in the absence of player agency, I agree - I've played that style many times and the initial post says as much.
Let me pose a question: do you agree there's an important difference re agency between each of these cases?
a) player A's GM is completely unpredictable and ignores player input
b) player B's GM has final say but is consistent and open to player input
c) player C and their GM are bound by the rules to roll dice checks to resolve any disagreements between them
If so, how do you describe it? I would say only player A has no agency at all. I'm not even sure C has more agency than B. It depends on the rules of C's game and the degree of chemistry between B and their GM.