You've completely missed the point I was naking abd mistaken it fir a confkation of player and character. I assure you I don't conflate -- player skill at acting has zero impact on my adjudication.
Instead, the point I was making is that all characters have the same ability to try to persuade another. This is "in kind." Some characters are better at it than others. This is "degree." When an argument is made about the ability in general, ie an in kind argument, then responding about how you handle a larger difference in ability is an argument about a difference in degree, not a difference in kind. Or, more simply, just a bigger bonus on an ability instead of a different ability.
Here, the ability is to persuade. The argument was that players determine if theur PCs are persuaded, not the dice. Your question about having a better chance of success using dice to persuade doesn't affect tge argument. Hence, it's a difference in degree, not in kind.
Yes, I react strongly to being told what my character does in 5e. I play other games where this is better, although even there it's more fictional blocking rather than changing my character's thinking for me, and I get a say in the failure outcome when stakes are set. Thise mechanics do not exist in 5e, so, yeah, I get what the rules allow only me -- the ability to determine what my PC thinks.
It's very difficult to see how wanting to use dice to control (or limit) another PC's actions (by either a PC or NPC) isn't a bad table situation. It's endemic of a flawed social contract and speaks to dominance rather than cooperation. Sure, on the OP the players have different immediate objectives, but how much time was spent looking for compromise before the player that had largest dice advantage asked for a roll to force PC cooperation? Why didn't the barbarian get a roll? Where they not disagreeing? Yet, it was the bard's player who asked for and forced the roll and expected the player to comply with his demands. This is a broken social contract, not a mechanics issue. The problem here sits around the table, not on it.