The reasons are pretty simple: taxes and racism. They use Birmingham as an example. Many of the pieces of land that seem like they "should" be part of Birming

The reasons are pretty simple: taxes and racism. They use Birmingham as an example. Many of the pieces of land that seem like they "should" be part of Birmingham were racist enclaves founded specifically to avoid desegregation. The land was restricted with whites-only restrictive covenants, and if they incorporated as a separate city, why, no one would force one city to bus their kids to an entirely separate school system run by an entirely separate city. Which meant that your schools, theoretically integrated, stayed fully whites-only (still are today). The Economist's bafflement at how this came to be is easily explained if you look at the history. I also see a bunch of carve outs where specific land owners have removed themselves from the city to avoid taxes.