Sounds to me like lots of these folks don't have access to what you would think of as a grocery store. I don't know that more public cafeterias and food kitchens would be the answer. Getting kids to the food when it's ready would probably be more aspirational than realistic. I'm guessing that things are pretty spread out, transportation and job schedules make that kind of communal living challenging. I don't mean to dismiss the idea because I see it work in my own community. During the summer any kid under 18 can get a free lunch in most public parks on the weekdays. It's a fantastic program and you can see that any number of people are showing up because they are in financial distress. Not only do the kids get a decent meal but they also end up exercising on the playground. You can use food stamps at many of the better farmers markets in our city. People with a food stamp card go to a central booth and get credits which they can purchase food from the vendors. The extra business from food stamps makes it possible for bigger markets with more variety to survive. It's capitalism and freedom of choice at it's best, not saying it's the only alternative but it's a good option for poor families.
Ugh I had a good response written out by hubski bugged out and it didn't post. The long and short of it was, I admit I haven't though this out entirely, but I have this feeling, perhaps naively, that there exists a much better solution to the problem. There's been a lot of increased food stamp spending in the past few years and I'm not at all convinced it's working.
I think that without the food stamp program there would be more severe hunger. No program is perfect but I think that there is more danger in the current political climent that food stamps gets gutted and replaced with nothing rather than a healthier alternative.