Beans and grains are cheap. Staple fruits and vegetables are cheap. Chicken is cheap (especially dark meat). Eggs are cheap. You can feed a family of 4 a very healthy diet for ~$100 a month if you're willing to put in the work sourcing and cooking.
That's the crux of the issue, though. Food deserts combined with a lack of nutritional and culinary knowledge - maybe a lack of time to prepare healthy meals - is what's killing the average American diet, middle class and below.
Side note: if you raise your kids on hot dogs, chicken nuggets and soda every day then you will possibly ruin their palette for life. We now have people that find drinking water disgusting, because all they've ever drank is Diet Coke.