To be fair, the Barbarian dialogues are usually marked Intimidation. I used the skill versatility Half-Elf mod and made sure I chose all the skills I wanted for my own version of Barbarian...which included Persuasion as my main charisma based skill.
I generally pick persuasion, although I have chosen Intimidation, where it thematically fit, and its yielded pretty good results.
Whether you are proficient in persuasion or not doesn't change the dialogue options presented to you though, right? A barbarian still gets a Barbarian-specific option that asserts your character to be a brute/uncouth/savage/gross, and no other classes get this option. And Barbarians get extra options to intimidate that other classes don't get, that should really be a skill check applicable to everyone. I.e., as a Barbarian you can choose to play otherwise, but as any other class you can't play as the personality Larian has chosen for a Barbarian. And the same for other classes.
Although that's an interesting idea come to think of it - perhaps instead of Larian tying certain dialogue options to Class, they could tie it to skill proficiencies. In the video in OP's post, perhaps those who are proficient in Intimidation get the "eat dung" option. Representative of someone who is truly creative and experienced with their intimidation prowess.
To be clear, I'm not saying ALL skill checks are dependent on whether you're proficient. Obviously lots should be attemptable without proficiency. Just the really
extra checks that show strong personality/expertise do.
