But New York City is just one of many cities across the country where this sort of cherry-picking happens. Public schools in cities across the country—schools intended to break down the walls typical of expensive, elite private institutions by opening up access to stimulating, quality education for kids of all means—are closed in their admissions. In other words, kids aren’t just automatically enrolled because they live in the neighborhood—they have to apply to get in. As a result, their student populations are often far less diverse than they should be. And, sometimes, kids who would otherwise be eligible for these schools never get to enjoy them.

New York City epitomizes the shortcomings of such schools, largely because of its unusual test-only policy. Still, although testing is a key force behind those shortcomings, it is one of several culprits when it comes to the flaws of selective enrollment in public education. Selective-admissions policies can easily shortchange disadvantaged kids when they include as criteria such as middle-school attendance records or grade-point averages and fail to consider non-classroom factors, too. Even simply requiring student candidates (and their parents) to be proactive, to take the time to fill out what are often laborious applications risks discriminating against the less fortunate.

National data on selective-admissions schools is limited—so limited that it prompted Chester Finn Jr., president emeritus of the right-leaning Fordham Institute, to conduct his own survey in 2012. The country, he discovered, is home to some 165 of these institutions—"exam schools," as he calls them—or 1 percent of all public high schools. These schools, some of which are centuries old, are concentrated in 31 states, including nearly three dozen total in New York City, Chicago, and Boston alone. All but three of these 31 states are located in the eastern half of the country, the outliers being California, Nevada, and Arizona. (Meanwhile, nearly half of all states have specific laws that set priorities for districts to follow when accepting students for open enrollment, according to the Education Commission of the States.)

Selective-admissions programs are in part symptomatic of a broader, three-decade-old reform movement that has aimed to overcome the "mediocre educational performance" of the country’s students as highlighted in the landmark report "A Nation at Risk: The Imperative for Educational Reform." They’re also an example of "school choice," the tenet that parents should have options when it comes to their kids’ education, even when it’s free. And according to Richard Kahlenberg, a senior fellow at the Century Foundation and the author of The Remedy: Class, Race, and Affirmative Action, cities often have multiple incentives for retaining or establishing selective-admissions high schools.