My solution:
1. Each character has an "Energy" called Acuity, which is derived from their Charisma, Intuition, and Luck stats, and it is essentially a measure of their mental sharpness and wit. As an Energy, it comprises one of the 4 possible Saving Throws.
2. Saving Throws have a unique structure: the entity imposing the throw defines the base target number that their target must meet by using the current value of the corresponding Energy they have.
3. At its most basic, any social interaction where something has been requested of another will require an Acuity save be made by the listener, with the speaker defining the target number.
4. To do this, they will first decide if they are going to invoke a specific Skill. The options are Provoke, Appeal, Deflect, Charm, or Insight. The first 4 are self-explanatory, but Insight also opens the options up to all 32 skills in the game, including general Talent values like Intelligence. Altogether they give characters a massive variety of options to approach their interaction, not all of which require any specific investment in charisma.
5. If they do not opt to invoke skill, the NPC simply makes an Acuity save against the players current Acuity, using their own Acuity as a modifier to their saving throw.
6. If the Player does decide to use a Skill, they will simply have to ensure that whatever they say does reflect or otherwise incorporate that skill, and they will be able to add their Talent modifier for that Skill to the Acuity save.
7. Based on what the player says in-character, the GM will then apply an additional bonus to the throws target number to reflect not just the "quality" of the in-character speaking, but also to reflect any elements of leverage or similar that would affect the chances of success, but not strictly be due to the skills involved or the NPCs own thoughts.
8. Whether the NPC makes the save or doesn't, they retain their own agency to still reject the request. This however, represents an "ettiquette" violation, which makes them vulnerable to things like peer pressure or even straight up consequences due to being irrational. However, they can circumvent this if they can identify that the Player was violating ettiquette themselves. For example, if the Player tried to decieve, and the NPC is able to prove it (even if only to themselves), they could resist the consequences of asserting their agency. And even then, they could also just be content in being belligerent, regardless of how this reflects on them socially.
9. These consequences will be reflected and reinforced in a Reputation system that combines rote awareness with sliding scale traits. Characters would have a specific Reptutation value representing how well known they are to others, and could have a number of paired, sliding scale based traits (such as Merciful <-> Ruthless) that act as a measure that those who know of the character judge them by.
This kind of modelling would make general sense and would naturally lead to the desire to find out what sort of person a person is if its important to succeed, but would also be able to be ascertained even in the moment (through Insight) to take the advantage. The different Social Skills could then be leveraged to exploit those traits and the characters Reputation.
While random NPCs like town guards wouldn't provide much of an interesting social interaction in this system (in much the same way that wolves stop being interesting past low level), more distinct or important NPCs would, as of course would the PCs themselves, who would be motivated to cultivate a reputation suitable to their preferences.
Overall, this system I think might just thread the needle on both modelling real life social interaction while also gamifying it in a way that respects both player and character skill. By restructuring how the interaction is resolved and repositioning what the individual dice rolls mean, and who makes them, this should avoid the issue of player and character skill clashing.
As players don't roll, and instead invoke their player and characters skills directly in order to pose a challenge to the NPC, with the values being derived from a mix of character and player skill, players who are good at being social in-character and those that aren't (but want to play a character that is) can coexist and won't overshadow each other or undermine themselves.
This system would also be benefitting from another baseline assumption of characters that, even at level 0 with the most minimal possible stats, every character is assumed as competant in all areas as the typical person in is in real life. Ergo, no matter who you are as a player, your character is always at or above yourself, so you don't have to worry about trying to step down to a lesser person, and if or by the time your character becomes exceptional at social skills, your Stats will carry you through.
While it will still be strictly optimal to do both, focus on social skills and be good at in-character interactions, this should ultimately be fine as the system is structured in such a way that the optimal play is the most immersive way to go, but also not the only way to consistenly succeed.