Intelligence is not a superpower

[martixy]

The ability scores in D&D do not form a complete coverage - saying e.g. that something is a cognitive ability so it must be under one of the mental ability scores would not follow.

Valid point. In general.
Practically, at the table, they probably do.

For example, the game mechanics to actually memorize a string of numbers is a trained-only skill. If you don't have ranks in Autohypnosis, no matter how high the character's Int, Wis, or Cha are, using a dice roll to memorize something cannot be done. Without that investment, remembering things is a function of the player's cognitive ability, not the character's. There is no roll to determine the correct spell that a character should cast in a situation - that's assigned to the player's cognitive ability, and there is no investment or advancement within the game world that makes a character mechanically better or worse at that task.

This is both true and false.

True in 3.5e, where the ability score description is a lot more spare and mechanically focused.
False in 5e, where Int explicitly covers memory.
(See OP's first post.)
So it's a toss up.

People usually don't stick to the rules that closely though. Most tables I've been at put memory under the purview of INT.
I do like however that a moderately good Autohypnosis bonus essentially gives you perfect memory. It's one of those unbounded game states 3.5 is famous for. Like pun pun and the d2 crusader.

So, in that sense, arguing that a character's high Int should let them get some game-mechanical advantage outside of what the game mechanics actually assign to the Int attribute is a form of 'cheating'. Same as if you argued 'well, super-human Dexterity means insane reaction times and super-fast reflexes, so a Dexterity of 40 should let a character run faster than the speed of sound' - when Dexterity, regardless of how it might be introduced, does not impact a character's Movement statistic.

Have I argued that somewhere?