I think what you said about self-teaching raises a good point. There are so many 'bad habits' you can get into when teaching yourself. Often you need someone else to criticise your proofs/essay/etc to help you improve. A good example is playing the piano. You can spend years teaching yourself from sheet music, but you might end up with shitty rhythm, or bad posture or bad fingering because nobody was around to be harsh with you when you got those things wrong. You can sound like Mozart when you're by yourself only to have your ego cut to pieces when you are told that no you should be doing it like this. That said, I object to you calling autodidacts "eccentrics" and "cranks". Maybe your conclusion comes from sample bias - most people with the inclination/mental ability/etc to teach themselves end up going to university because it is the Done Thing, thereby leaving the slightly odd people to represents autodidacts. This would actually be a pretty interesting thing to investigate...
Underwood Dudley wrote several books about cranks in mathematics. Their prevalence is one of the reasons we don't have many contributions from amateurs in mathematics anymore, despite being a discipline with a history of important contributions from amateurs; so many mathematicians get letters giving oddball and fallacious proofs of statements already proven to be false that amateurs are just assumed to be cranks. Dudley's books are still encumbered, but libgen has them. Here's De Morgan's much less sympathetic study of 19th century cranks.