Where I stall on this is the implication that when someone is hidden, and a character fails their passive and active perception checks, they just need to... look more intently? It implies that some but not all skills have no effect on characters. What I dislike there is the picking and choosing.
An alternative is that how they follow the suggestion is up to the player. Player and DM can consider consider factors like how long the persuasion might last, and what might erode it. Right after the conversation, the barbarian feels convinced this would be a good idea. Later, when someone else questions it, they start to have doubts. There are so many ways to play this I find the notion that the barbarian never makes a decision for themselves to be of course understandable, but actually only how it looks on the surface, before player imagination is applied. The face is a natural leader and the barbarian needs strong reasons to not follow that lead.
Doesn't "virtually" amount to setting an appropriate DC? I think one complaint the barbarian can have is that a contest against their unmodified Insight doesn't capture what was asked. From their perspective, helping the villagers meant sacrificing something else they wanted to do, and perhaps taking a risk. Maybe they're helping people that as a barbarian they see as intruders on the land. They could have argued for disadvantage on the Face's check, and in at the same time, in some cases, advantage on their own, to capture their reluctance. And if they find themselves constantly being "played", then downgrading their relationship from friendly (as allies) to eventually hostile (which could add +5 to their check, on top of disadvantage/advantage looking at the DMG). As they have time to dwell on how they just keep getting lead into things they don't at heart want to do. A neutral observer, like a Bard or Cleric, might feel concerned for their easily-led friend, and offer guidance.
Social skills are consistently an area where, perhaps due to lack of nuance in the mechanics, groups often feel cautious of saying - these apply equally to monsters, NPCs and PCs. Yet my overriding feeling is that it is exactly events like this - prompted by dice rolls - that can create roleplaying opportunities.