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.