Most importantly --- players understand.
If you dump STR, DEX, or CON, you can't role-play your way out of it. You aren't your PC. You can't go break down a door in my house because your PC failed to break a door down in a dungeon. (Well, I guess you could, but it won't help your PC any, and you'll have to pay for the door!)
So, you can't just "do things" for INT, WIS, or CHA via role-play simply because you, not your PC, would be able to. Consider solving a riddle or puzzle. A low INT martial PC isn't as likely to solve it, even if you as the player can. Now, you can certainly ROLL for your PC to solve it, because then the low INT will come into play. This is why for many such things I prefer group checks, because often the players (as a group) are also working together.
Ultimately, if a player insists that their PC convinced the guard, solved the riddle, should have found the secret door because the player said their PC looked "right there", I just tell them, "no." If you want your PC to be good at such things, because you are (so to say), then put your ability scores to favor them, take the right skills, etc. If a player can't accept that this is how I run my game, then most likely they will enjoy playing with a different group (or at least when someone else is DM).
You are playing a character, not yourself.