So 일반적 can mean 'normal' or 'general' (both adjectives)? Can it mean 'usual'? Is the 일 prefix derived from the word for 'day'? So this means something like 'the normal/usual/general/daily theory'? (As opposed to 'the abnormal/unusual/special/restricted/once-in-a-blue-moon theory'?)
I really like your hypothesis, it makes perfect sense to me, but there, 일 represents another Hanja.
일반 - 一般
일 - 一 - whole; entire;
반 - 般 - sort, kind, class.
일 like a "day" is 日, it also means "sun."
There is also native Korean 일하다, where 일 doesn't have any Hanja counterpart.
일 also means "one" and the Hanja is "一".
Really recommend Wiktionary when you are looking up Hanja. Links lead to Witnionary pages.
Hope you'll find it useful.:)