Sacrosanct
Legend
The DM can only call for an ability check when there's uncertainty as to the outcome of a task. The task here is "Convince barbarian to go along with rogue's plan." Players can't call for or decide to make ability checks.
The question is whether there is uncertainty as to the outcome of the task. And the answer is: There isn't. A player determines how the character thinks and acts - thus the outcome is whatever the player of the barbarian says it is. With the outcome being known, there is no uncertainty, and the DM therefore cannot call for an ability check to resolve this matter.
That's just your opinion. Mine (and others) for example, would be "this is a role playing game, and role playing means to play your character as if they were a living actual being, which includes things like intelligence and wisdom." In that case, then it very well is reasonable and justified to make a roll like you would with any other persuasion check in the game.
Some people ignore role playing aspects and don't force players to play their character like an idiot if they have an INT of 6, while other groups do. Your position is hardly objectively the one true answer. Not saying mine is either, but that since it's subjective and a matter of opinion, making rolls is a legitimate way.