NASHVILLE—This city has been a poster child for economic development, the good and the bad.

Tax breaks and cash incentives have flowed. Tourists, sports teams and conventioneers have come. Hotels and restaurants have bloomed. And now Amazon.com Inc., among the most-sought-after employers, is erecting a pair of towers downtown to house 5,000 new employees, a move the company promises will “further the resilience, the vibrancy and just the overall coolness” of a place once known only for music.

...