1) Scripted social conflict where the players' role (through their PCs) is tip-toe around and cater to/placate the unidimensionality of an NPC in order to access a "content/info dump" completely subverts any idea that the PCs are protoganists with thematic interests that should emerge through and propel play. The only party with thematic interests that will emerge through and propel play in that model is the NPC! They become the protagonist for the conflict! If that is true (and I'm quite confident in that arithmetic), does anyone actually think that is a good model to follow for TTRPGing? If you do and you agree with that assessment above, I'd love to hear why.
I'm not sure what thematic interest is served by interrupting a negotiation, but sure, you can remain the protagonist and insult the Mad Tyrant. Just don't complain when the consequence for doing so is unpleasant. Nothing about what happens needs to change that the PCs are the protagonists. The problem seemed as much as anything to be that it took the campaign far enough outside the published adventure that the OP didn't feel comfortable ad-libbing (mostly because of how that table games on VTT, as I understand it--I think maybe there weren't maps ready). Well, that and the players seemed to have different ideas of what their goals were at that point.
Why would someone who writes an adventure EVER create a unidimensional NPC that must be dealt with in a very particular way? Even the most "paranoid strongmen" have nuance to them. They have a person (perhaps a few) that they secretly respect beyond all others from which admonishment is actually meaningful. They have regrets and shame that are buried away but are capable of being unlocked and brought to the fore. They have deep fears that can be made manifest that can have them press the nuclear option (flee or suicide). They have egos that are profoundly fragile and lacking resiliency such that a serious challenge and then a following through makes them question their autobiographical depiction of themselves in their heads.
"Don't insult the Mad Tyrant" isn't so much "Deal with the Mad Tyrant in one particular way" as "When dealing with the Mad Tyrant,
don't do this." There seems to be some conflation of these two things, and there's nothing in your description of his potential personality that invalidates his reaction in the OP's specific case--weak leaders lash out, not strong ones, and IIRC he's specifically called out as weak.
Why can't/doesn't a GM arrange this strongman's Ideal, Bond and Flaw with something like the below:
Ideal - The people recognize my efforts are for their own good and they love me for it.
Bond - I trust the Captain of my Guard more than anyone in the world; perhaps more than myself.
Flaw - Reactionary narcissist.
So (a) if you have a PC that does exactly what the PC does in this game (calls him out for being a tyrant unworthy of ruling this people) and (b) the player succeeds on his Charisma check, why can't literally all 3 of these IBFs manifest as a result?
* The NPC calls for his Captain to arrest this fool. The Captain (who suddenly becomes the intersection of the PCs successful check, the Baron's Flaw, and the setting at large) pauses and says "...he says nothing different than what the people are saying in the safety and privacy of their homes sir...arresting him will not sanitize that image...it will further sully it." After which, the Baron clearly shrinks and blanches while he gathers himself (after which the GM will either reframe the conflict with his next move from the Baron or another NPC present, or a player can make a follow-up move to reframe things).
* The player has changed the gamestate functionally (the players can now use IBF machinery to leverage action resolution success for the rest of the social conflict) and interestingly while expressing a thematic interest (maintained protagonism), the NPC has changed as a result, the setting has emerged through actual play.
Why is what happened in the lead post preferrable to the above? For 5e D&D or any system?
Huh. So, I suppose a DM could arrange those traits for the NPC. Maybe those fit the descriptions of the realm in the published material; if not, the environment would need re-writing to suit those (and I'll let that slide for the purposed of discussion).
The impression I got from the OP was that the CHA checks were related/directed to the Mad Tyrant, so we're getting even more counterfactual here by having it aimed at the Captain; but I'll play this game for the nonce. If the Captain is so much the focus of the Mad Tyrant's Bond, he seems as though he might need fleshing out the same way as the Mad Tyrant, and he needs to be the sort who'd earn the Mad Tyrant's trust, keep it, and not act out before now. It's at least as easy to write those so his Bond is, e.g., "An insult to my Lord is an insult to me" as anything else; maybe his Ideal is "I will do what I must to keep the peace between my Lord and the citizens" and his Flaw is "I keep my Lord's trust by keeping my silence." Now we have an NPC who'd be the sort of quiet sideman who'd be the focus of the Mad Tyrant's Bond, and keep his position and other wise fit into the setting as described. And by insulting the Mad Tyrant, the PCs have triggers the Captain's Bond, and made it much harder for them to persuade him not to arrest them.
See? Anyone can re-write the scenario to be anything.
In reality, what you've proposed isn't a bad way for things to go. I wonder how many NPCs a given player would have to insult into submission before someone started feeling the verisimilitude slip away, but that's a matter of taste. I kinda feel, though, that focusing so much on Ideals, Bonds, Flaws, and Traits kinda seems more like NPC as Puzzle than something more ... freeform, but it doesn't need to be that way in practice, I suspect.
What happened in the OP is preferable to your counterfactual if--and only if--the table wants "realistic" play and if--and only if--that's what they consider "realistic." Note that it doesn't seem as though the players felt the Burgermaster behaved unreasonably or unrealistically.