So how is it okay that that's the case with INT and WIS and CHA, but not with all stats? This is a clear double-standard, and one which isn't apparently well-supported by any kind of actual rationale beyond "I want it thatta way!", to quote the Backstreet Boys.
Yep. A low wisdom might be foolhardy or absentminded or oblivious. There is no, might be very wise. Those "mights" are right in line with the what abilities represent sections with ability checks.
You are adding to the game that which is not there.
5e lacks the prohibition against (fragrantly?) using out of character knowledge, like 1e and 2e do. That means that by 5e RAW the player can have the characters thoughts reflect the players in terms of critical thinking skills, knowledge of the monster manual, knowledge of tactics, reciting romantic poetry, etc... So the only time the INT, WIS, and CHA rolls are needed by raw is when the character is attempting an act with a chance of failure ("My [5 int fighter] attempts to recall his days of studying engineering so he can disable the trap.") as opposed to the character acting on something the player had them think of ([after hearing the description] "My [5 int fighter] pulls the third level on the left after I have the other fighter pound a wooden wedge into the gear.").
I'd house rule against flagrant uses of OOC knowledge like that, but others would allow it and say it causes no troubles at their tables.