I built a character with all CHA skills (Deception, Intimidation, Performance, and Persuasion) so I could get the maximum value out of the character's 20 CHA and Tirmar Paladin build (+7 on all CHA skills, plus advantage on Intimidation and Persuasion if they use their power).
When there is more than one CHA skill option in the dialog, that character only uses one of them - the other characters 'take' the others, usually with a far worse bonus. It appears that when there are multiple CHA skill options in a dialog, each option can only be used by one character.
There are three problems with this:
1) There is no obvious reason for it: This is not a 5e mechanic. More generally, it is fairly normal for a party to have a high-CHA 'face' who does most of the NPC interactions because they are good at it.
2) This makes a large part of a build like that useless - sometimes the option you want to use is taken by a character with a much poorer bonus.
3) It punishes good character design. Especially for characters built on point buy, probably only one of the party will have a good CHA, so it makes sense to give that character all (or most) of the appropriate skills.