It's not, because America is highly segregated by self-increasing difference in school quality (because more expensive homes in the area yield more property taxes to the municipality which are used to fund school), and better schools make richer people move to the place, driving up both home prices, and school qualities too by improving racial and social mix of students, and it goes on and on in a self-propelling virtuous cycle. As a result most places are strictly segregated and no, children from all backgrounds don't go to the same school because they don't live (poor can't afford) in the same school district.