As far as I can know, food prices in America have gone down a little bit in the long term in comparison to general price index; 1982 food price index was 100 and now it is 90. Where I live (north Europe), the price drop has been more substantial.

The biggest health problem that poor people face in the U.S. is obesity.

But even if food is not problem, the real issues are housing and health care costs.

As said, real estate prices have gone up. But in early 1970's, Americans used 20 % of their inćome on food. Now it's somewhere around 6-7 %. So, for this most basic of commodities, the purchasing power has increased substantially.