It would seem to me that in such a case, there would seem to at least be the possibility of fear being an issue.
Why?
I am usually more fine with fear, as it is easier for me to "force" to feel, but I actually (vaguely) remember one instance from some old game (I think it was some sort of White Wolf hack) where this caused serious disruption of immersion to me. I remember my character was this weird shunned goth kid who might have had some special powers, and then the GM described some sort of supernatural apparition (I have forgotten the details.) And for that moment my internal model of the character said very clearly that this character actually is not afraid of this, they are thrilled, exited and interested, and would approach the weird thing (with which they felt sudden kinship.) But there was some mechanics that said my character would be afraid instead and should hide or something. It ruined the cool moment and ruined my immersion for the rest of the session at least and permanently damaged my connection to the character.
If you get to choose the outcome, then it’s not a risk.
But you don't choose the full outcome. You choose your character's stance. You don't choose what the king does once you betray him, you don't choose how the other knights feel about it, you don't choose how the queen will feel in the long run etc.
Again, look at combat. There’s risk in combat because you’re not just free to decide the outcome. It’s out of the player’s control.
But it is not. They choose the tactics, they choose what powers to use, how to move, all sort of things. If the outcome was just determined by a dice roll, there indeed would be no agency and it would be very hard to get invested in that.
I want the players be making choices, hard ones preferably, and I want them to be immersed in their characters and feel the weight of those choices. I don't them to passively observe what the dice say the character feels or does.
Like I don't know, I really have never found gambling appealing, especially if it is just random, but a lot of people are literally addicted to it. So this might be just some sort of psychological quirk. Some people probably can get highly invested in randomised fates, whereas for me to get invested requires me to be deciding things, to be actually making hard choices.
I don’t know. Again, this doesn’t sound like something that happens in play. Is this some kind of situation where there’s like a bluff or deception check by the guard? Again, I don’t know of any games that work this way… but I’d just tell a player “he says there’s nothing beyond the wall… and he seems sincere”. No need to tell the player what their character believes beyond that.
Then we do not disagree on how this sort of thing should be handled, so stop arguing with me about it!
My point is that you are capable… any player is capable… of ignoring their personal response and crafting a response for their character that’s different.
And in the process to ruin what is most important to me in the game. I mean I could, like I could throw the dice out of the window or intentionally pour my drink on the GM, but why would I? I am not gonna do those things. And any game that forces me to do that is a terrible game in my book.