The majority are not homeless but rather shut-ins, uncared-for elderly or suffering from other mental health issues.
As for the adults, maybe we can write sleep outside until you freeze, get shot/stabbed, or jailed where you're threatened with sexual assault and are in general treated like a disease until you acquire enough money to escape the poverty trap and possibly mental help, the least funded area of America's inhumane medical system that is one of the top reasons people go broke.
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.
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
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!
Excess mortality is often hard to pin on its actual cause. If you can imagine 100 people in 2 alternative universes. One in which they are well fed, have access to medical treatment, get normal sleep. Another in which they are tossed on the street where they eat poorly, sleep poorly on a cold corner and live poorly.
In the second universe they don't drop dead of being poor on the spot or tomorrow they just gradually die a lot sooner.
Its much harder to drum up enthusiasm to fix. There is a 60% chance that 7 out of 10 of these people will die an average of 10-20 years sooner than it is to save someone who will die next week.