I wonder how many people play a low Int, Wis, and to some extent Cha as just the player's abilities with the character's modifier if a roll is needed. A player may be a genius and playing a fighter with a dumpstat of Int. There is no real penalty of playing the game with the strategy and meta gaming of how to go about things and piece clues together. It seems that every PC is the extension of the player in these mental abilities so the only problems in when roleplaying something less.
This can be tough. If I'm playing a PC with low int or wisdom, I try to not make the intelligent or wise moves. However the problem is that there are times when the guy playing the genius level PC doesn't see something obvious or doesn't understand tactics at all. Sometimes I'll say something out of character, sometimes I won't. It's why I rarely play low intelligence PCs. Unwise PCs it's easier because I just play them as not picking up on clues or being reckless and so on.
But it's also one of he reasons I dislike challenges that challenge the player only. If the sphinx asks the riddle "What has a golden head and a golden tail but no body?"* You're challenging the players, not the wizard with the 20 intelligence who really should be able to figure it out with no difficulty.
On the other hand a lot of times people seem to want to play against type as wish fulfillment. In my experience a lot of people who play wizards tend (and this is only a tendency) to not understand how to use their powers effectively. Doesn't make anyone less worthy as an individual if they aren't particularly smart, but I do find myself biting my tongue about how they have spell X and if they had done Y it would have been so much more effective. But I don't tell people how to run their PCs except occasionally with newbies if they seem to be struggling, even then I tread lightly. In any case, there are always going to be limitations, going both ways, of how well we can represent our PCs.
*A gold coin.