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Acedemic schools in the old world worked purely on Rhetoric and Memorization (people like Einstein are NOT a product of that kind of education, ‘never memorize what you can look up’) (1 AD/1000 AD focused on YOU being the encyclopedia, we now know encyclopedic knowledge of things is (extremely) detrimental to the brain, especially its development (rote memorization is aweful for your mental and emotional health, though beneficial for technical repetitive skills(which are terrible for you body!).

Philosophy was also mostly that, though a few schools of philosophy taught otherwise, so likely there was a random very private/selective/in lusivd schools scattered about scarcely. But this would have been rare and hidden ‘free thought’ in the old world quickly snuffed out because free thought destroys well kept/maintained status quo like monarchies, government, etc… schools today don’t teach or encourage much free thought. Literacy was especially rare to learn for non-nobility/priest class because literacy was POWER and influence during those times (but this is what made Greece and Rome rather amazing since literacy and education was rampant!)… but just remember 1 AD Rome’s population height was 1 million (largest population in the world!) out of around maybe a billion people total in all the world (mostly slaves or tribal folks, mostly in India, china, and the americas) so you are looking at ~1.7 million educated people per 1 billion.

But come the age of mass literacy (not quite modern schools but post Victorian times) up till the 1900s or so (your great great grand parents high school-college education was roughly equivalent to what’s completed by second to third graders now a days) schools taught arithmetic, literacy, various languages, hosts of domestic skills (critically important), religion, etc.

Come the modern age when school houses had classes bigger than a single class room. All the life skills learned by grade 2-5 (usually 3rd), literacy, functional math, etc. DONE. The focus shifted for schooling to be about SOCIALIZATION. More importantly it’s about learning to get along with other people in your area/in general if you have a diverse school, GROWING UP with those people, and most importantly especially in college(this is what college has always been about since the post renaissance era) it’s about making network connections.

These social opportunities provided by school in the modern era NEVER HAPPEN NATURALLY except as very rare flukes so, if this main aspect is acted upon intentionally, it opens tremendous world of opportunity for every single student. However re: loner outcasts who don’t at least find a misfit group gain only detriment from modern school.

Incidentally throughout history those who WANT TO LEARN find a way as they entirely self teach (teachers remark about this about their exceptional students, that they the teacher rarely did more than inform them the library/internet/books exist).

Pre-the written word the ‘educated’ were exclusively self taught or taught by someone self taught, etc, And ALL information that has been passed down was original from self learners.

Learning is its own reward for them and someone interested in learning is born that way, nothing stops them. Schools can make it easier (more time to spend learning, short cuts through an environment where asking questions might be okay (it rarely seems to be however)). More downsides than upsides to schooling for self learners though (unless they are very interested in networking connections too).

Incidentally: your success or failure in everything in human social world (or ‘the world’ of humans, jobs, money, etc) is based on who you know. This is especially true of the opportunities all those positive people talk about. If you don’t have connections or sometimes large social circles very few chances for opportunity are even possible. THAT is the purpose of school.

TL;DR: The purpose of school is for building social connections so you have access to opportunities. Ancient schooling was trash, take off the nostalgia glasses(apprenticing was and still is amazing and as it has always been it’s still readily available).

If you integrate different ways of thinking about things (mindsets(logic based) or looking at things (perspectives, nonlogic-processing trees/patterns/shortcuts) or combinations of those it ADDS TO your intuition by adding additional paths or circuitry (reinforced/new/improved/additional purposed neurons/myleinsheathing,etc)

But those things don’t become ‘inuitive’ (again you are describing with your words several different other things, which are correlated but not actually intuition/intuitive)

Something ‘it just make sense’ is intuitive, something not making sense and then suddenly making sense is a product of intuitive processing/intuition.

(To be more formal. Not that language is capable of expressing intuition correctly (only approximately/indirectly): Intuition is the result of data processing in the brain of sensory information you are not (typically, but re: hallucinogens, epilepsy, special brains(unique envrionmental influences, ADHD(hyper connected brains),etc), very atypical brains(genetic/mutation/damage/newstructures other mammals don’t have/etc) privy to with conscious awareness on the logic/linguistic parts of your mind, you can train your intuition indirectly (increase its accuracy, etc) as well expand the areas that it will work on(part of what you describe in your article). But what you described in your article is only basic skill training to develop automatic or ‘global’ skills (think about how ‘riding a bike’ is a global skill) all what you describe does involve one of your other thinking modes that is not your logic-thinking mode, which may be why it’s giving you the impression intuition is involved, but intuition is only a specific process of those other areas of your brain, the things you describe are yet other distinct processes (that your intuitive brain may or may not use depending on their value for intuitive proccesses).

I get the impression you spend too much in logic-thinking mode and neglect all the other modes of awareness and/or thought, so when ever you aren’t in logic mode it feels ‘natural’ (it is true that it is natural! Logic mode is the weird kinda unnatural mode when used improperly!) and seems to flow and come easy, and you think that’s intuition because intuitive things also feel like that. Essentially anytime ones other brain modes take over or do a task AND logic becomes chill and submissive (or rather especially when it does), that happens and everything comes easy, smooth, with flow, etc. however intuition is only one of the processes in one of those modes(although all the non L-mode modes use it heavily, L-mode CAN access it too by stepping down from dominating the others).

TL;DR: nothing in your article (indirectly or directly) describes intuition or intuitive processes, however it does describe products of and a sub processes of intuition influenced stuff. Further you (appear to) have mind/experience problems with using your Logic Mode thought process in unhealthy/detrimental ways where any slip into one of your brain’s many other modes of thought/awareness feels ‘natural’ and you conflate that with intuitive stuff (read whole post for explanation).