While it may be common, it certainly isn't universal. I've worked in schools in poor communities that have pushed for good educators. In one of those schools, the push for better teachers was by the students themselves. There are plenty of good kids and good parents in many poor communities.
I'm not sure the opposite is true either, i.e. that expensive homes are a proxy for good schools. I've also worked in schools where the families were affluent, but the environment was toxic due to the behaviour of students and parents.
> There are plenty of good kids and good parents in many poor communities.
I went to school in a poor district. Pretty much all the students at my elementary school were poverty adjacent. Most of them were good kids, but that didnt really matter because the 10% who werent often ruined it for everyone else. This is a one bad apple spoils the bunch scenario, so the incentive is to make it as hard as possible for even 1 bad apple to be in the school. Of course there are plenty of bad apples among rich kids too, but as you can imagine the politics is different there.