I would never say "change to whatever" ...
To have option to roll persuation with dexterity is worse than bullshit.

(maybe unless you are trying to persuate someone that you are agile enough for something

just kidding)
That is why i listed few examples there and kinda hoped that people will either stick to them, or add their own.

I mean, maybe i understand it wrong bud based on what i have read (
https://roleplayersrespite.com/dnd-5e-ability-scores) ...
It seems to me that Intelligence is more like regular study ... you lock yourself somewhere with a book, and if you have high Intelligence, you are practicaly able to memorize it whole.
Wisdom on the other hand seem to be more like common sence, or connecting contextual dots ...
Let me give few more examples:
1) Nettie reach for that root, or twig, or w/e that thing is.

On sucessfull Intelligence roll: "You recognize that plant, its *XY*, highly poisonous ..."
On sucessfull Wisdom roll: "You dont know what plant it is, but you dont know any plants with such thorns that are not dangerous ..."
2) When you read Loviathar priest inside goblin camp:
On sucessfull Intelligence roll: "You know this kind of worshiping, this man is priest of Loviathar ... maiden of pain."
On sucessfull Wisdom roll: "You realize that this man mumbles some mantra, while he was whiping himself ... is this some kind of worhiping?"
3) When you find that book of Gods.
On sucessfull Intelligence roll: "You remember those names, this is list of Gods!"
On sucessfull Wisdom roll: "You dont know those names, but something within you responce to them ... as if there was something divine on them."
etc. etc.
Also i would not have any problem if this alternative rolls would be accesible only for related classes ...
I mean, Cleric should have enough life experience to at least "have better chance" to recognize something divine, when he looks at it ... even if his Intelligence (and therefore Religion) checks are low.
Druid should have enough life experience with nature to at least "have better chance" to recognize some plant, or at least guess its purpose ... even if his Intelligence (and therefore Nature) check are low.
Barbarian should seem enough frightening, so his very presence should be intimidating enough ... even if his Charisma (and therefore Intimidation) check are low.
Its all about context.
And quite honestly, i would not even mind if i had to pass a little more dificiult check, or if passing that alternative check would not give me all the information i would get with the first one.
All i want is a character that is in contextualy logical situations able to pass both battle, and conversation checks without sacrificing effectivity in either. :-/
Right now for my Druid i have to decide if i want to be good in Dialogue checks (Int) ... or battle (Wis) ... and that just dont feels right to me. :-/