IMO players should feel like badasses. Rolls are for when they’re doing something the hero in an action movie might fail at. This doesn’t mean that the game shouldn’t be challenging, but rather that the players should feel challenged by powerful foes, not by mooks. Thus I think the solution is simply not to require a roll when an ordinary person would have the skills to succeed with certainty. The barbarian would automatically succeed (at least on the surface level) in this situation.

I would only require a roll if:

• The intimidator isn’t obviously frightening or dangerous. The halfling bard would have to roll unless he’s scarier-looking than the average halfling.
• The intimidator is trying to be subtle. The barbarian would have to roll if he doesn’t want to make a scene in public.
• The intimidator is trying to get the target to stay intimidated even after the target is not in immediate danger. The barbarian would have to roll if he doesn’t want the guard to run for help as soon as the barbarian is out of sight.
• The target is unusually resistant to intimidation. The barbarian would have to roll if he’s threatening a fanatic unafraid to die.
• The target might tell a convincing lie. This is the fun case, because a failed intimidation roll will look like a successful roll until the barbarian walks right into a trap.