That's how it is in Germany for primary schools. If you move across town, your kid has to change school. But kids can choose secondary school, which then selects based on grades.Just think of all the traffic it'll take off the roads if children are just made go to their nearest school. None of this wank about trekking halfway across town because it's "WHERE FATHER WENT".
Schools are all resourced to meet the needs of whatever kids attend them now. It's normal to have all sorts of demographics in the one building. Segregating by class is completely stupid and only creates further division with an "us and them" mentality.
US also has school districts but I'm not sure it's the best model.