Food availability is a solved problem in the United States. Portraying it as a problem takes resources away from real problems which need to be solved.
If you take it merely as a question of caloric intake you're right. If you're talking about the cost of high-quality and nutrient-rich food, there's a long way to go. The massive subsidizing of junk food through corn subsidies does not help, but if you try getting those calories through vegetables and quality meat you may find it's out of reach for many people, and that does have an impact on intelligence and development, especially when those cheap calories lead to obesity, diabetes, and other complications.
Unless every fast food restaurant is outlawed and shutdown and all crap food is outlawed and removed from the shelves of every store in the U.S., you are not going to stop anyone (low income or not) from eating it.
And for those on WIC, while many crap items aren't on the WIC list, parents can still abuse it by buying things like only Cheerios for their kids to eat instead of veggies, etc. And yes, regardless of welfare, Obesity and diabetes are going to remain very common among the poor in the U.S.
...especially when those cheap calories lead to obesity, diabetes, and other complications.
If you are purchasing too many calories, you are wasting money that could be spent on veggies.
Poor parents raising their children badly is a real problem that should be solved if we want to improve the next generation. One possible solution is to constrain the food choices of the poor - replace food stamps with food boxes and fill the box with only healthy options.
This is already done through the WIC program. If you look at the shelves in the grocery store, you'll see the WIC label on certain foods. It does not stop poor food choices. The only way to make it work would be to shutdown all fast food restaurant and pull all crap off the shelves in the store, and that will never happen. Anything that can be abused to get more caloric intake for less money will be abused.
The poor in the US do not suffer from a lack of food availability.
5.1% of poor children don't get enough to eat. For comparison, 5.7% of children above 4 x poverty line don't get enough to eat.
http://mchb.hrsa.gov/chusa11/hstat/hsa/pages/221oo.html
Food availability is a solved problem in the United States. Portraying it as a problem takes resources away from real problems which need to be solved.