there is a very big difference between studying things on my own and being physically at a school with someone who's an expert to guide me.

It's something that I've learned from #tfgsworkout: once there's little to no social pressure (especially from various sorts of patrons, like teachers), forcing yourself to learn becomes hard, even if you're passionate on the subject. Like you said: it's not impossible, but it becomes difficult to stay on the same level. I suppose, personal teachers (what's their name in the US?) should do the trick, even if you have to pay them (which means they're only a financially equal opportunity for would-be university students).

basic physics and mathematics is all that is taught in secondary schools, at least in America.

Do those include logarithms and integrals?

Also, what basic sciences are taught are never taught to apply to daily life: I can extract that I can use geometry (or whatever the proper field name is) to compute the necessary angle to cut stuff at, but physics and chemistry - two very powerful sciences in one's apartment or house - are simply pushed as information, with little to no regard for whether there'd be any use of it (which there must be). Given basic daily-oriented electrical physics education, for example, one can probably get their way into DIY-electronics and fix their own electrical mechanisms properly. Otherwise, what's the point of learning this stuff?

Discipline may or may not relate to education. Certainly, good mentors will push you to perform even as you don't feel like it (a bullshit reason, but many of us don't recognize it for what it is), but they mustn't reside only in schools. Jobs may have them, as well, and if it's a job you excel at due to your sheer interest, you only need a little bit of motivation - often more than enough when extracted from the job results - to stay on track. Overall discipline can be achieved on your own; like learning, it will become more difficult to stay on track when you're on your own, so some support (or your personal drill sergeant) is necessary; schools may or may not give it to you.