In fact, the U.S. actually provides incentives for companies to use high fructose corn syrup: https://news.ycombinator.com/item?id=5795478
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.
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.