Is there some sort of in-between here? I totally get what you're saying, but taken to its conclusion, wouldn't that mean no one could really play an 18 CHA bard (for example)?
Well, yes, I do feel it's very hard for people without a lot of charisma to play a character that has a lot of charisma. You can get part of the way by having a mechanic that allows successful interaction based on a die role, but you can't get all the way and actually also have a realized transcript of play.
So, yeah, you could probably have a game where someone says, "I use persuasion on the guard.", rolls a dice and then successfully gets the guard to do something. But then the question arises, what did that character say that so persuaded the guard? There is no actualized transcript of play here. There is no movie playing out in the participants head. There is really less of a transcript of play than, "I hit the guard with a big stick." At least that causes you to imagine something.
And as you attempt to create that transcript of play, you find that some people not only do a better job, their understanding of social dynamics and their natural charisma helps them in much the same manner that a player with a strong understanding of tactics is better able to succeed in combat. They understand what levers to pull. They understand what not to do. You tend to find socially awkward people saying socially awkward things in social situations as well, and there is only so much having 18 CHA on the sheet can protect them from that - in much the same way that an optimized combat twink can succeed despite their poor tactics but still can get in over their head. I have had any number of times where a supposedly charismatic character lied when the truth would have sufficed fine, tried to intimidate rather than persuade, told the truth when a lie plus all that points in social deception would have worked better, insulted characters rather than befriended them, and generally just acted a jerk. Yes, 18 CHA lets you get away with that more than 8 CHA does ("Coming from anyone else...") but there are limits or the transcript of play just gets silly, and often a game system will differentiate between persuasion, deception and intimidation and a player will for whatever reason just rely on the one not actually on their character sheet.
There are also something you just can't pull off with a die roll. As a GM you become really aware that no matter how much charisma you give an NPC, if you can't make an NPC likable or funny or whatever, then no amount of telling the players the NPC is funny or likeable matters.