"Questgiver" NPCs absolutely cannot be intimidated through dialogue until you either complete or fail (probably by lying to them and getting caught) their missions.
You can reproduce this by running into a dynamic spawn NPC and seeing if the first thing he'll do upon chatting with you is to give you a mission to kill his zombie mother, kill a jabberwock, get him antibiotics, etc.
You could always accept the mission and then lie about it, but that would be particularly dangerous when you're in the middle of a forest and a NPC is asking you to kill a jabberwock. Accepting results in the Jabberwock spawning nearby.
It would take less keypresses to mug a questgiver if I could simply intimidate him right away. Something like this:
Would be better solved by removing the whole important quest thing or only allowing it to be important the first time the player talks to the NPC.
Fixed by #28050
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Would be better solved by removing the whole important quest thing or only allowing it to be important the first time the player talks to the NPC.