> The best all-income schools are catholic schools, averaging at 1 grade level higher. Then private schools do even better

These are not equal comparisons. People who send their kids to a private school are choosing that, and thus care about the education their kids get. While Catholics are all income and choosing for religion reasons, generally catholic implies cultural care for education. Public schools take everyone including those who don't care about education.

In general public schools in the US are very good. However a small number in every school are kids that would be kicked out of private (including catholic) schools. There are also significant variation between schools with richer areas of a city doing better - despite often spending less on education.