Some city schools are excellent, and business case for a private or a charter school is stronger in a city. There's also wider availability of various after-school programs.
There's the space concern for those who wouldn't mind a backyard and a pet or two, safety concern associated with letting the kids just play outside, transportation concern as far as effort required to drive them to school and various after-school programs.
This stops being the norm when desegregation occurs. Now that all races must be allowed to mix in schools, businesses and housing, whites flee to the suburbs, put up giant financial barriers in the form of zoning, and refuse to be annexed.
These days overt racial politics is now dogwhistled as concerns about crime or undesirables or culture. But that's a big heaping portion of why things are the way they are.
(This only really applies to suburbs within the same state of the main city; New Jersey, most of which is suburbs, would not face the same annexation pressure since the main cities their suburbs are part of (Philadelphia and New York) are not in their state and can't legally annex them.)
Your comment is contradictory. On the one hand you say that crime, who is undesirable, and culture ate incidental and have nothing to do with race and then in this sentence you acknowledge that American history was largely determined by race, although you use very passive language as though that "shaking out" was some benign, incidental process instead of the cruel and brutal system it was.
But there is a difference between saying people are primarily motivated by race vs. primarily motivated by class but using race as a proxy vs. primarily motivated by class only. Given that these are distinct things, it's not helpful to insist on identifying everything as being secretly racist, not because it conveniently absolves anyone of responsibility but because it muddies the discussion and denies possible solutions.
In terms of $/sq.ft. an urban residence in the US will almost universally be priced higher than a suburban one. There are a few exceptions to the rule (Atherton might be pricier than SF, Beverly Hills pricier than LA), but in general if you have a fixed price point in mind, suburbs will get you more space for your dollar.
http://www.washington.edu/news/2015/10/07/new-uw-report-pain...
Here's a list of top 50 cities https://en.wikipedia.org/wiki/List_of_United_States_cities_b... It does not include Baton Rouge, Chula Vista, Chandler, Cincinnati, Cleveland, Fort Wayne, etc.
You can sort of see why - without Chula Vista, Chandler, Stockton, Cleveland, Pittsburgh, Toledo or Raleigh this thesis https://www.crpe.org/examples/six becomes much more muted.
It also measures public schools exclusively, ignoring the fact that urban communities are predominant attractors of private and charter schools - their business model makes less sense in suburbs or rural environment.