"Can I roll high enough on the dice" is hella boring way to test one's beliefs to me. Instead create a situation where the loyal knight has to choose between betraying his king or betraying his true love. That's a real test of character and outsourcing the decision to the dice would utterly defeat the point of playing the character. I want to play the character, not just passively watch how they act as dictated by the dice. That is the crucial difference between RPGs and other media: we get to choose.
If that choice is taken away from me, I'll just hand the character sheet and the dice to the GM and leave; they can roll what my character does next.
I agree with you.
I came up with a solution that works for me for this when designing my game Other Worlds. In that game, social conflicts are not about whether the character is
persuaded about something. They are about whether the character is able to
win the argument with the other person in a way that represents the social pressures inherent in such a situation.
So, if other people are there - maybe it's a formal audience with the King, a meeting of the different captains, or a carousing scene in a busy tavern - the roll determines whether in the eyes of those onlookers you won the argument. If it's just you and one other person, it's about maintaining a good relationship or reputation of friendliness/competence with that person. If you lost the dice roll and therefore the argument it doesn't mean you are persuaded by the merits of whatever the other person said, it means that social pressure is forcing you to go along with it. You can still do what you want - but there will now be
consequences to not going along.
An example people might relate to is a work meeting where a change is proposed that you think will be counterproductive. Someone puts forward the argument in favour, you raise points against, and then there is discussion until it feels like one side has carried the debate (i.e. won the roll). You are on the losing side. 'No, we hear you about your concerns Crimson Longinus, but we will be careful and issue appropriate guidance, this will improve our numbers next quarter so it's agreed, we will do it'. In my game, your character would now get a flaw called something like 'Everyone Else Agreed to the Stupid Thing'.
Now, what can you do about that decision? You still think it's a bad idea. You can quit. You can refuse to implement the change in your own part of the office. You can try to get a do-over by raising it up the chain, getting more data, starting a petition, trying again next meeting, etc. But all of these are uphill battles because you already lost the argument. That initial persuasion success by the other side means that your new flaw 'Everyone Else Agreed to the Stupid Thing' will act as a penalty to you in your attempts to subvert or resist the change. You risk looking like a bad loser, being ostracised, missing promotion opportunities, getting disciplined, getting fired.
Or, you can just go along with it, and maybe mutter 'I told you so' when it all backfires on them a few months later.
So in a way the player's situation neatly mirrors the character's situation. You lost the argument but were not persuaded. Now you either accept that or you escalate things at a penalty in the hope of a do-over.