That's true to an extent, but much less true of Catholic parochial schools. In fact, such schools will sometimes have a population with average income less than the local public schools. Of course most parochial schools won't have special education programs, so that's a huge filter, but as I pointed out doesn't account for the budget gap.
In any event, "picking your customers" is exactly the point of the previous poster(s). Money doesn't really explain what we're seeing. Once upon a time there was a very strong correlation, and people presumed causation, but now it's quite clear that the causation wasn't there. Certainly not directly, which is why throwing more money at the schools isn't helping.
Money can be extremely strongly correlated but if I get to kick out the bottom 20% of shitheads I can still outperform you on half the budget. Not talking income wise, talking behavior wise.
Sounds similar to charter schools in NYC. They often get better results than public schools but because they “manage out” kids with bad behavior and/or learning disabilities, in a way public schools cannot.
Some public charter schools do the exact opposite, take in the problem kids so they can be given an environment better suited to their challenges. For example, Gateway Highschool in San Francisco. And they have better outcomes for those kids. But better is relative, and they get alot of criticism from those convinced equity demands the whole student population be perfectly shuffled across all classrooms, and who argue having such options excuses the district from providing even more resources to the average classroom. Many of those same people also work to prohibit ever removing a problem child from a classroom (see recent controversy in SF, about schools secretly doing that despite city prohibitions on suspension or even class removal), arguing instead every classroom should have 2 or 3 additional instructors, as if that would magically cease the disruptions.