Perhaps school meals should be free?
My children go to a private school, where school meals are 'free' (i.e. the cost is included within the termly fee, so no extra charge). 99% of children eat the school meals. Including my own coeliac children, and several others with allergies/intolerances/vegetarians etc. The food is all cooked on the premises, is good quality, and special requirements are taken care of.
I think perhaps school meals, of a fresh, healthy type, should be paid for by taxes. Allergies and intolerances should be catered for.
Parents could choose to send children with packed lunches, but since this would cost extra, I expect the majority would not choose to. I think this would be a better idea than forcing children to. There will always be some cases where a packed lunch is required (a poster above with an ASD child who needs the same lunch every day or becomes distressed, for example)
When I was a child, at my village primary school, we all ate school lunches, it never occurred to anyone to do otherwise. When my children were diagnosed coeliac, it was really important to me that they were able to continue with school lunches - i see it as a social, educational, health thing. The communality of all eating together, at tables, with cutlery and good manners, the nutritional benefits of a proper hot meal, the socialisation of eating a wider range of food because they see their peers eating them - it feels like a core part of the day to me.