I see where you're coming from, and more power to you if that works at your table. In my mind, Charisma accounts for how you present your arguments and how receptive people are going to be, not the contents of your arguments. It's totally valid to say your character could make better arguments than you, but that would depend on intelligence or wisdom (depending on whether they're logical or emotional arguments). So we would typically break character to figure out what the arguments are going to be.

When characters have higher intelligence than their players, I typically collaborate with them in a form of pseudo-metagaming, acting as a supplementary brain for the character. I readily give them / remind them of relevant facts and suggest things that I think might work. For high wisdom characters, I would let them roll an insight check to get a better idea of what emotional arguments might help.

With this, the player can form their arguments before I decide whether we proceed or roll. I realize this might sound tedious, but I think it works well as a way for my players to RP high INT/WIS/CHA characters. And we wouldn't do this for every conversation, only major ones. Sometimes we just want to move things along and I do just assume the character would likely come up with a decent argument, and ask for a Charisma (persuasion) roll

or even Intelligence (persuasion) or Wisdom (persuasion) if it seems appropriate.

I'm not saying our way is the correct way, it's just the way we do things and it works for us. My players don't find it to be unfair.