Putting healthier food on school cafeteria menus has done little to change school lunch participation rates: By my calculation, roughly 20 million eligible children, mostly from middle- and upper-middle-class families, continue to opt out of the national program by bringing lunch or by buying special à la carte food items not covered by the program.

As an individual family decision, packing lunches might seem like the best option, especially for children with special dietary needs. But when millions of families do so, their actions reduce the political will and financial resources necessary to make public school lunches better for everyone.

The Trump administration isn’t much help. According to Agriculture Secretary Sonny Perdue, providing schools with the flexibility to plan menus that appeal to students’ taste preferences is a way to attract more paying customers to the federal program and reduce food waste. Mr. Purdue has pursued this strategy for making school lunch “great again.”

In practice, this has meant enacting policies that loosen restrictions on the amount of sodium, flavored milk and refined grains that can be served in school meals. The department’s own data shows that participation in the national lunch program is higher in cafeterias that serve healthier meals, yet the administration’s latest proposal, released last month, would allow schools to serve more French fries and fewer green vegetables.