At least in America aren’t school taxes extremely local? I’m not sure what you are suggesting actually happens, or at least you are exaggerating quite a bit.

Poor people typically don’t live in the same neighborhoods as wealthy people in America. Wealthy neighborhood public schools tend to have lavish facilities from the tax base, so it’s more like “wealthy guy X doesn’t want to pay for the very fancy facilities he isn’t even using”, not “wealthy guy X doesn’t want to pay to send his poor neighbor’s kid to school at all”.

Where I live all the districts in the metro area pool the money and divide it so the poor student is worth just as much as the rich student in a different district. (Assuming you don't go to a private school)

There are still schools rated much worse than others.