Last May, the families of students at Cypress Academy, an independent charter school in New Orleans, received an email announcing that the school would close when classes ended the following week and that all its students would be transferred to another nearby charter for the upcoming year. Parents would have the option of entering their children in the city’s charter-enrollment lottery, but the lottery’s first round had already taken place, and the most desirable spots for the fall were filled.

Founded in 2015, a decade after New Orleans became the nation’s first city to begin replacing all its public…