In my city, there are 5 high schools in different parts of the city. There is a huge difference between the rankings of 2 schools compared to the remaining three. Funding and teacher pool are pretty much the same source. The main difference is the students and their families. The parents in those areas are well educated and have high income. If anything the best performing schools looks like a dump compared to the 3 lower performing ones. I'd say student background plays a huge part on their performance.

> They do find a correlation, but it varies substantially between countries, suggesting that other factors are at play.

Sure, but we’re talking about what explains variation between school districts in the same state in the US, not variation among OECD countries. I'm not saying that education policy and practice can't have a difference and doesn't globally, I'm saying there is virtually no evidence that the difference within districts that people in the US might be choosing between is driven by much of anything beyond background.