Poverty in the US is NOT the same as poverty in Somalia. It's not even the same as poverty in Estonia. Childhood hunger is the best example - malnourished children in the US are in that state because of abuse.
Anyone that grew up in a truly shitty North American neighbourhood in the last 20 years knows - the people that were suffering were not suffering because of a lack of resources. They made bad decisions, or had health problems, or were abuse victims.
As for the homeless, I would posit for that 20-70% with behavioral issues, we can start at least by offering medicare for all so their symptoms can be treated. Secondly, for the 80-30% who are merely unhoused, the solution for them works quite well!
Careful your sodium intake, rinsing the beans can reduce it by 40%, outta luck for the fish.
(good comment btw)
https://www.healthline.com/nutrition/how-much-sodium-per-day
I personally grew up in a single minimum wage income household, which supported 2 adults and 3 children. I'm very familiar with dubious food. That said, it is quite reasonable to meet the caloric needs of a grade school-age child in the United States with little regard for taste or variety for roughly a dollar a day. Adding some variety and nutrition to that wouldn't be much more. Formula for very small children averages between about $40-$100 a month so they are a little more expensive, but you did specifically say school children.
There are 50 lb bags of rice at my local grocery store for $15. I have bought them before, they're short grain and not very good so you wouldn't want it everyday, but in a pinch you can meet your caloric necessities with rice for basically cents.
I actually don't have a very strong sense of taste, and manage to get by on ~$3-$6 of food a day, my diet consisting largely of over-hard eggs, canned fish and canned string beans. I am quite confident I could get by on half of that if need be.
As far as homelessness goes, I don't have reliable statistics on this, but depending on where you get your statistics between 20 and 70 percent of America's homeless have mental health issues.
I am perfectly aware that this is anecdotal, but I have a friend who worked for an organization that housed homeless in unoccupied Homes and Apartments. According to her, the majority wandered off because they did not understand what was going on. In Minnesota no less, it's cold.
My point is simply that there is a sizable portion if not majority who cannot be helped without stepping on their personal freedoms, because they won't allow it, for better or worse.