EzekielRaiden
Follower of the Way
I would argue that it is quite possible for a highly intelligent person to make mistakes. That is, Wisdom is associated with judgment, not Intelligence; the former is about soundness of judgment, while the latter is about speed and precision. But if one wishes to take this route, there's a simple mechanism: Give the player with high Intelligence (or Wisdom, or indeed any stat, not just mental!) more leeway with one of my absolute favorite questions as a DM:So what about the reverse? How many Int 20 Wizard players are super-geniuses? When they do stupid things, should we police their roleplay by saying "you're too smart to do that"?
"Are you sure you want to do that?"
It has other variations ("Did you actually do/say that?" for when they've joked around and you want to be sure whether it was a joke or not; "Is that what you want to do?" if you aren't sure whether the player is actually enthused; etc.), but it is almost always THE most powerful tool I have for shaping player behavior.
A character with 20 Strength must know their way around using that strength, at least to some extent, even if they lack formal training. It seems reasonable that they would be slightly more likely to "know their own strength" as it were; not guaranteed, but more likely. So you give them more benefit of the doubt, give them a wider window of opportunity to pull back from something questionable or to reevaluate their decisions regarding whatever stuff they're good at. This respects the stats in question, without "policing" their roleplay, at least in my opinion.