I would not be upset if the viceroy wants to throw my character in the jail, I would be upset if the social combat forces my character to change their mind about the viceroy being evil, and instead makes them think that the viceroy enslaving the gnomes is actually a good thing.
So, the idea that social conflict resolution should "change your mind" is an artifact of the incredibly and woefully simplistic and reductive approach to social interaction currently used in D&D. That's not what social conflict resolution ought to be.
Social conflict resolution is "getting what you want by means of social interactions", rather like physical conflict resolution (aka "combat," in D&D) is getting what you want by means of violent physical interactions.
Does the orc "change your mind" with a sword? No. So, we don't need the Evil Viceroy to change the PC's minds in a social conflict. What we need is for the Viceroy to be able to get what he wants through social interaction.
What does that mean? Well, for an orc on a battlefield, getting what he wants means removing the PC from the battle - in D&D, by reducing them to zero hit points. So, in a social conflict, the Viceroy needs to remove the PC from the field of
social battle - make it so nobody will listen to them or take them seriously. If the Viceroy can successfully make the PCs look like fools, liars, agents of a foreign power, or simply woefully misinformed vagabonds, then nobody will pay attention to their pleas. The Viceroy has to
reduce the PC's social cache to nothing, so they cannot change the situation by social interaction.