I'd say it would be more relevant if high charisma ability check bonuses offered alternate conversion choices, but that wouldn't really be fair either because you can say whatever you want in Dnd. The DC is what really prevents a low CHA character from pulling off ridiculous diplomatic choices in a convincing way, not their ability to come up with it.
Intelligence and wisdom should also count to offer options. I mean charisma is how you say things and has to do with persuasion, but wisdom and intelligence might help to say things that make more sense to the other person, hence, lowering the roll difficulty. But I do undestand how that might be too much work and limiting to some players. I think charisma is covered by the persuasion and deceive rolls.
