I might be misunderstanding the problem but in Australia the parents send the kids to school with packed lunches proportional to the household income… fancy lunches for rich kids, and rice or bread for poor kids.
a sandwich is enough for a mid morning snack, but not for a midday meal unless the kids get another meal right when they come home. traditional wisdom has it that you should have a good breakfast and lunch, and a smaller meal for dinner. that's possible when the kids come home no later than 2pm but if they usually come home at 3-4pm or later then a sandwich is not enough to get them through the day.
the official US guidelines for school provided lunch range from 550–850. that's a bit lower than i would choose based on daily needs especially for older kids. breakfast and lunch should be more than 1/3rd each. dinner should be less than 1/3rd.
i am from austria. a sandwich here is considered a snack. not a meal.
This could also be an overseas perspective because in my opinion (having just returned from USA) the single meal portions are very large in USA compared with overseas.
I took a packed lunch to school almost every day. Later on I packed it myself. If I wanted the canteen had hot meals. Sometimes if you forgot your lunch they would give you 1 meal on credit.
IIRC there's a program in the absolute poorest aboriginal communities to provide free hot lunches at school, because it nearly guarantees attendance and works towards defeating malnutrition. I dont think yanks are that hard up yet but who knows.
Somehow the yanks are constantly demanding free lunches like there's no alternative or workaround?
~75% of k-12 students bring lunch from home. If you are on assistance then your lunch is prepaid. Generally the food is so hilariously bad that most won't pay for it, but there are good schools here and there. 9-12 students generally are allowed to leave campus during lunch hours.
There may also be an additional "a la carte" system where you can buy single items either if you have extra money in your account or have cash on hand, but not on credit. Like a canteen.