A 20 int PC can go up to int based problems that he has NEVER seen or heard of and solve them with a fair amount of reliability.
Just to be clear: are you saying that a 20 INT character can know that William the Conqueror's reign in England began in 1066; or can know that the Nile is the longest river in the world; even if s/he has never encountered those facts before?
That seems odd to me (and in discussing the first "knowledge check" mechanic in the game, thieves' Read Languages ability, Gygax said (DMG p 20) that "This ability assumes that the language is, in fact, one which the thief has encountered sometime in the past. Ancient and strange languages (those you, as DM, have previously designated as such) are always totally unreadable").
Ask yourselves if you were statting up characters of fiction, how would you rate their intelligence - Would you necessarily give Hodor a low Intelligence? Would you necessarily give Sherock Holmes a high Intelligence?
If the answer is yes to those questions and you choose to interpret your character's Intelligence score differently, it isn't because you don't consider Intelligence to mean intelligence, but because you wanted an easy dump stat and don't want to have to deal with the connotations involved with dumping that stat.
Does your opinion also stand to the opposite end of the spectrum?
For example, you have a 20 Int character that does not have proficiency in any Int-related skills. As a consequence, he barely has a 50:50 chance at success with a medium difficulty task that is intelligence-based.
Does the fact that he has reached the limits of potential for human intelligence inspire you to play him as the genius that his unparalleled levels of intelligence suggest he is, or does the fact that he is barely adequate at not particularly intelligence-based tasks inspire you to play him as someone of average intelligence?
There are at least two things going on here that I find puzzling.
One: what does it mean to "play a character as a a genius with unparalleled levels of intelligence" if you have only a 50/50 chance of success on medium difficulty INT-based tasks? You are not the only poster to have introduced this notion of
playing a character as a genius in some fashion that is divorced from succeeding at INT checks, but I still don't understand the notion. Can you give an example of what this might actually look like in play?
I think the reason for my puzzlement is, broadly, this: I've known some fairly clever people over the years, and the way their cleverness manifested was in the ability to succeed very reliably at the intellectual endeavours they set for themselves. So in the context of the game, I don't know what it would mean to be very clever yet not be very reliable at intellectual tasks.
Two: the example of "Holmes with 5 INT" is
not about statting up a character from fiction. It's about statting up a character, playing that character, and then having it emerge in play that the character in question is very clever. There's been a long discussion upthread of how that might happen even if the PCs' INT is not terribly high (eg lucky rolls; good skill bonuses; avoiding the need to roll at all via skilled play; etc).