It would be preferable to think that our players would roleplay the stats they have selected for their characters, and that if they "dumped" a mental stat that they would play into that fact as they play their character (since quite frankly, I think roleplaying into bad stats can be a lot of fun). And I agree with it to the point that on the rare times I get to play, I purposefully choose classes that work on high INT or I raise my INT stat even if it isn't "beneficial" per se for that class to do so... all so that I can be okay with playing to the best of my ability while still maintaining a truth in the fiction. So for instance my paladin in the Pathfinder game I've been playing in actually has a lower CON than one would ordinarily think a warrior class would have, just so that I could put a few more points into INT because I wanted to RP him as a halfway-intelligent fellow.
I kind of like to think of your game stats as giving you characterization that one should bring out in play. It's part of the unique kind of fun of TTRPG's, honestly - there's a REASON this hobby resonates with so many theater kids, and one of the big ones is that it scratches that performance itch a little bit, the fun that is in figuring out who a character is based on some evidence on paper and then pretending to be
that person instead of yourself. The dice and the stats help guide that performance, but they don't really constrain it.
A big part of the fun of D&D is pretending to be a magical elf for four hours on a beautiful spring afternoon. The social pillar is one of the best places, in play, to scratch that itch.
Which is part of why "social combat" mechanics often fall flat, IMO. The social pillar is Drama Club. The combat pillar is more Math Club. And that's fine, and both work together to create a sort of mental pacing that itches different parts of your brain. A D&D that was all Drama Club or Math Club (and there are PLENTY of fantasy heartbreakers that go one of these routes) is overall a weaker experience for it.
...and Exploration is History Club, in this metaphor.
But that being said... as a DM I don't really care if the players at the table really bother playing to their mental stats or they don't. One, because I'm not really bothered by "dump stats" that players take... and two, the difference between a stat that has been dumped and one that is completely normal or adequate is like just 3 modifier points. And when it's the die roll that will swing numbers between 1-20 points... those 3 points of the ability modifier don't have nearly the same effect in comparison to warrant me getting bent out of shape over it.
So if players take an 8 in INT because they need to save their points for DEX, CON, and WIS to play what they feel is an "effective" character... I'm not going to police them when all the players at the table start trying to formulate plans and they chime in. It's not worth it to me to get that far into the weeds over it.
Because suspension of disbelief is pretty important for Drama Club, I like when there's
some justification. But it doesn't need much.
If the 8 INT barbarian's player just came up with a clever solution to the puzzle, I'd want them to invent some sort of in-character excuse for it. Maybe, the puzzle solution was clear to them because their bully of an older brother who was always smarter than them punched them in the arm every time they were unable to answer that
particular puzzle. Or because the solution reminded them of hunting an elk for some reason. Or whatever. Because it's a moment of characterization, I want some characterization, and an unusual success is a time for some characterization! If the characterization was lacking a bit, that's when we might roll to find out what happens - if the 8 INT barbarian can put these together. This rewards good role-playing because it makes the moment something about the succeeding character
This is also a time I might use the OOC table-talk as a sort of brain trust
for the characters with higher INT. Like maybe the 8 INT barbarian's player comes up with a solution, but in practice this just gives the solution to the 18 INT wizard's player, and then the 18 INT wizard is the one who came up with it diegetically. None of us players are 18 INT, so I'm pretty OK with representing a high mental stat as linked to the best solution several people can come up with.
This style works for most mental stats. The 8 CHA grizzled mercenary might have a genuine moment of bond with someone for some reason, and if the player can make the game overall better by linking it to their character, then that's the kind of behavior I want to encourage. If the 18 CHA bard isn't bringing that, that's OK - they have an 18 CHA so when we call for a roll, they're still likely to hit it. OR, if the mercenary's player wants to give that answer to the bard and have the bard do it in the story, that's collaboration and is also the kind of thing I want to encourage. OR, for wisdom, if an attentive player noticed something odd in the room description, I'd want them to investigate, even if they're an 8 WIS rogue (or give it to the high-WIS ranger).