In Canada we use that model for funding schools, it’s set by the province on a per student basis with adjustments for special needs.
In BC private schools get (or used to get, govt changed recently) half of the funding of public schools.
I don’t know if the issues are to the same degree, but they certainly exist. That said I vastly preferred the poorer school where we got to wear hats to the rich area school with more rigidity.
It’s funny too as in my area the private expensive Christian schools would shuffle off their pregnant teenage moms (the rates were alarming) off to the poor school that had the teenage mom program. So to me education solves a lot more problems than income for sure.