I've grown to dislike ability scores that indicate personality or the intelligence of PCs, for various reasons. For one, it makes certain personality choices highly punishing for some characters. If you want to play a smart or charismatic fighter, you'll be punished by being less effective at your role. Of course, you can just roleplay your character that way regardless of stats, and I see this done constantly. Does that mean players roleplay their character "wrong?" Or is the stat wrong?
There's that situation where most of the party is silent, because they're afaid of screwing up some social encounter as they side glance at the party bard. "What are you doing, barbarian? Trying to role-play in a role-playing game?! Now make a Charisma roll. That'll teach you to make the bard do all the talking!"
Then there's the trouble with role-playing characters of different intellect than your own, which (hopefully) is never really enforced anyway. "Oh, you think you just did a clever plan to stop the ogre? Well, your Int is only 8, so your character wouldn't do that! And why haven't you come up with a brilliant idea no one else has thought of yet, Gundalph?! Your character has 18 Int! Start role-playing like it!"
If we separate things like charisma and intelligence from from ability scores and mechanics, the player no longer has to sacrifice "fun" to play a desired personality. But then we don't have a lot of stats left, do we? Well, if we look at D&D, Wisdom is not really a personality stat anymore. It's more of a Perception or Awareness stat. So maybe it's just a question of renaming, or looking at abilities through a different lens. Intelligence could be "Knowledge", reflecting study, observation and practical experience prior to adventuring, rather than reasoning and logic. This also makes sense in terms of additional skills and languages gained, which the ability does in some systems/editions.
I struggle more to get around some kind of social stat. For some classes, it just makes sense to have one. Like a bard or leader archetype, such as a warlord. Perhaps use a stat with a more neutral name, such as "Presence" and simply have it affect the initial disposition of NPCs. Interactions past that could be handled purely through role-play, rather than die rolls.
The problem of personality/intelligence stats goes double for systems (or tables) that emphasize "player skill" and seek to test the imagination and reasoning of the players.
Should some characters just check out of the role-playing game when it's time to role-play? Should the GM keep putting the shy player with the high Charisma score on the spot? Should the GM berate an average intelligence player for not coming up with genious plans all the time when playing his 18 Int Wizard? Should he make the Int 3 cleric walk blindly into the dark room and onto the pit trap? How many stats should there be at minimum? Do I even have a point, or am I just over-analyzing and rambling? Make up your own questions and add them to the list!