So you're really hitting on the different qualities that can exist inside of public education here, and it's definitely a state-by-state issue (although universally I'd say there are systemic differences between the quality of public urban education vs. suburban vs. rural). While that's definitely a topic of concern and a big problem, the fact remains that that is still publicly funded education. "Rich districts" are still funded by state & county tax funding, where those tax payers are directly taking advantage of their tax dollars at work. My objection was just this notion that public education is just some fringe social benefit for the poor, because outside of the mega-wealthy, its one of the few places in government that society is very deeply invested.
There is thst: society benefits from educated kids, but we've managed to create a system segregated by socioeconomic factors that tend to inhibit social mobility, which then describes why the US can simultaneously have the best and worst schools in the developed world at the same time.