It's incredible how easily we overlook everything it takes to do what you said.
Yesterday I was talking to a friend who recently had a baby. He's an educated, employed, white, probably wealthy, smart, guy who loves good food and knows how to cook and lives in wealthy suburbs. What he said yesterday was along the lines of "I totally understand why people eat fast food so much. I drive by Jack in the box on the way home and, while I haven't done it yet, the idea is compelling."
So here's a guy who "knows" that it's bad to eat fast food. and doesn't want too. But he's tired from his 9-5 desk job, doesn't sleep as well as he wants to do to the newborn), and doesn't want to cook at the end of the day.
What if he was a high school graduate with a physical job making $35k a year with 2 kids who doesn't live near a grocery store and never had any exposure to cooking, food saving, and all the other things you have? What is the chance that person, on their own, is going to discover their horrible diet, learn how to prepare and save their food, break the habit of sugary foods, etc.
Just because you can do it doesn't mean it's easy, or common sense, or even possible for a huge swath of the population.
Thanks for having empathy. Hopefully comments like yours will help other people see what they're lacking.
So basically, the numbers only work out if you're living somewhere cheap (i.e. not urban). Where I live, a chicken that feeds four costs $8-$15 (roughly $2 a pound). Eight meals means two birds, plus the cost of everything else.
You can argue that it's cheaper to feed a family with careful shopping than to go out for fast food every night, but there's no way that you can get that many of the meals described for $20. You could maybe do half that.