Becker-Posner do their usually thorough job discussing the arguments for and against government involvement in fast food choices. They include discussions of possible external costs.
But, thorough as they are, their discussion does not quite touch the logic of the LA City Council. This morning's LA Times includes "Council bans new fast-food outlets ... Officials want to bring eateries with healthier fare to South L.A. ... Councilwoamn Jan Perry, who as pushed for a moratorium for six years, said the initiative would give the city time to craft measures to lure sit-down restaurants serving healthier food to a part of the city that desparately wants more of them."
No externalities here. When and where people "desparately want more" of something (and less of something else), that's a job for local government.