Thanks for providing the full quote (which I had also provided further upthread). Your interpretation of that is... interesting. As if the character creation prescribes how one must play their character. Again, nothing wrong with house-ruling if you're having fun with it.
I agreed with that above - if people want to ignore their stats and house-rule that you can play your super low intelligence PC as if they had a high intelligence except when making rolls, nothing is stopping you and it can be a lot of fun.
Now, please quote the rule(s) in 5e where it says the players must play their characters according to some strict definition of their stats.
Pg 175-179. Without any hedging language, they tell you what your stats represent. This has all been discussed upthread - a few times.
(Hint: check out p14 of the 5e PHB, the "Your Character's Abilities" part of the Describe Your Character section... you'll find a lot of "might be"s and "usually"s and "probably"s. Nothing is written in stone of how someone must describe or play their character.
The hedging language here is used to indicate that you may have alternative representations of the way the high ability score may manifest. It is saying, "Hey, here are some mainstream interpretations of high ability scores." It is not saying, "Feel free to just ignore your scores and have a low intelligence PC know every fact about every monster, spell, and magic item in the books, while having the full force of Google helping them solve riddles."
Of course, most people will play along with those ideas because it is fun to do so, but a DM needn't get themselves worked up if a player has a different interpretation of how they want to portray the stats of their PC.)
A DM runs a game for two players. Characters are generated using point buy, both are non-Variant humans. One PC ends up with 16s in the physical stats and 9 in the mental stats, while the other has 9s in the physical stats and 16s in the mental stats. One is a fighter, the other a Wizard.
The PCs go out and start adventuring. They come to a bridge over a chasm. The high ability score PC navigates it easily. The low attribute PC struggles to get across. They realize that some monsters are nearby and hide - the fighter has no trouble, the wizard is spotted.
Then they reach the dungeon. There is a riddle to open the dungeon door. Both players listen and the fighter player solves it before it finishes. They enter and the fighter player realizes that the far side of the main chamber is the perfect spot for a trap, halting the duo from advancing. After avoiding the ambush, they encounter the hag and try to persuade her to help them. The fighter player realizes that she is trapped in the cave and they can free her in exchange for her help.
The fighter steal the spotlight from the things where the wizard's stats say they should excel. Further, this dumb, foolish, awkward fighter is coming off like a smart, wise and savvy negotiator. Is that something that should be addressed? Or, as the fighter do you just want to tell the wizard he was an idiot for worrying about mental stats?
And yes, I do recognize there are times rolls are called for - and yes that is a balancing component to the abilities. That is my main point, actually - that you should be using those ability scores to determine success for the mental challenges PCs face. You should not have PCs ignore these ability scores when they do 'mental things', and if their mental stats are low enough they should struggle with some things most of us take for granted that people are expected to be able to do that are not so easy for everyone.
People in 5E call intelligence a dump stat for almost every PC at the same time they're failing to respect how the books describe it being used. If any player can just recall what they know from the books, or use their potentially vast real world knowledge to their aid, then there is no point in having mental scores - but we do. We always have. I bet D&D always will as a sacred cow.