My understanding --admittedly limited-- is that in Japanese, people say as much as they can with as little words as possible. So I wondered why ないだろう would be used in everyday speaking instead of まい? The latter seems shorter and easier to use than the former.
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To answer the question in the title, yes, it is generally only used in literary text and, I would say less often, on TV. It could also potentially be used in a really formal speech or something like that.
I remember in my 9th or 10th month of studying the language I tried this out on a Japanese friend, saying something like
Sure, it's fair to say that users of the Japanese language tend to shorten things a lot, but that's not to say that the shortest way is always the normal or "modern" way. For example, the archaic form