It has more to do with parent involvement and support, and after that, community support. If the family does not value education, then the likely kids wont. Poverty in and of itself plays a role. Poorer families have other stressors that distract from school, and poorer families tend to not know the benefit of education (they may have been told education is a ticket out of poverty, but few see it happen). And it spreads out of the home. In poverty stricken areas, the majority of peers will shun those who are academically excellent as some kind of sell out. There have been successful schools in poor areas like Harlem when the majority of parents and students care about their education. On the flip side, excellent schools pull in families that value school performance and those families support and push the students. Annecdata: I grew up very poor and made it well into the middle class, it can be done, but the cards are stacked against you.

Why would you think that similar people living near each other is the result of a coincidence?

Abject poverty is likely to have way more impact on kids performance in school than any level of school funding. Whether you want to lump that in with "children's efforts" or not, it's certainly exogenous to the school.

Or 3. The humans who are smarter become richer and have children who are also smarter (and thus do better in school).