I used to live in a downtown area and it was nice being able to walk 6 blocks to work. But I would never want to raise a family in an apartment or with those terrible schools.
a school in a rural area isn't automatically better than a school in an urban area because its rural.
If less people commuted into the city from the burbs urban schools would get better for the exact same reasons the schools are often better in the burbs now.
Most urban areas have a mix of terrible and excellent schools. The excellent ones rival or exceed the best of the surrounding suburban schools (except with more in-school variance in terms of quality of instruction and background of students), while the terrible ones are truly toxic. Conversely, rural schools are more uniformly "meh" -- generally not toxic, but also pretty underwhelming in terms of instructional quality and available learning opportunities/resources.
Also, IMO, test scores are not great indicators of school quality. Even if you could perfectly control for all confounding factors, test scores probably still wouldn't be great indicators. They're simply, de facto, measuring the wrong things.
Or better yet, say something constructive.
If rich people move into the cities, and form little neighborhood clusters to exclude poor families, the schools will become more attractive by all standard measures.
Now, the trick is that it's much easier to build out segregated wealthy communities in the suburbs, than it is in cities, since tight geography works against the informal segregation of suburban development projects.
I guess that system is designed in part to account for the effect you're describing - if one school starts to become known as a better school, the kids in the poor parts of town are just as likely to be able to get in as anyone else. I have no idea if it actually works that way, but I do know it's a pain for my sister who now has to drive her kids to school several miles away when they could easily walk to the closer one. Can't please everyone, I guess.
Be careful there at teasing out the real motivation. If you want "wealthy students" because poor people are icky, then you're a jerk. If you want "wealthy students" because you want schools to be well-funded, that means you do in fact want good schools.
How to tell the difference? Maybe by putting the person somewhere where all schools in a very large area are funded at the exact same level. I don't know. But assuming it's a dog whistle isn't a good idea.
What's your definition of "good schools"?
In many cities, poverty is highly concentrated not only in urban areas but also in some of the surrounding suburbs. So the suburban schools -- or at least some of them -- end up as bad or worse than the worst of the urban schools.
So the old surburb/urban school quality divide is slowly breaking down. As a result, affluent urban areas often have high quality schools while impoverished suburbs often have terrible schools.
That said, it's generally true that living in the "good" suburbs is cheaper than living in the "good" parts of urban areas.