The Food Stamp Program started as a way to help people whose shelves were empty. It certainly helped my family. My mother was a single parent who struggled to make ends meet in wealthy Darien, Conn., during the 1970s. We relied on food stamps until I was 16.

Since then, the program has grown considerably. Renamed the Supplemental Nutrition Assistance Program, it supported more than 40 million Americans in 2017. Even though SNAP is generally well-intentioned, what it puts on shelves is not always helpful or healthy. SNAP rules...