I believe it's been stated somewhere that EY draws primarily on the skills he had around 18 and intentionally keeps things from beyond that out of Harry's reach. So Harry is more like a brilliant high school student than an adult (and, extra seven years worth of rationalist training aside, the way he approaches problems is a lot like a middle schooler with superpowers: "I can win, you can't, deal with it, 'cause I'm awesome and you know it." Which manages to annoy everyone in-universe and out.). Time isn't really a problem, either, if Harry has nothing else to occupy his time; exercise and social interaction are apparently not his thing, and he wound up out of the public school system after a few years, so he really does have way more time than most kids his age to read all the books. And he has that mysterious dark side and that sleeping disorder, whatever those contribute.

The other strangely adult-like children, however, are not so easily justified. (Draco gets most of those complaints, from what I've read.)

I wanted the maths behind relativity and QM at age 10. And I wasted a lot of time in school.