It has more to do with the income level of the families sending their kids to a school rather than the funds that the school has available.

This is why the only way to successfully reduce inequality in the education system is to reduce inequality in society at large.

That doesn't even make sense. We've seen lots of positive outcomes from increasing funding directly to less-well-resourced schools.

We have to defy rich people's preferences to do that, but that is entirely possible.