I hear what you're saying -- I think there are a few points here:
- Obesity is not isolated to food deserts. The people in food deserts may be in a pitiable situation, but most of us are obese; not just the people in food deserts. If obesity were isolated to food deserts, or even concentrated in food deserts, I might feel differently.
- Even the people in food deserts have access to nutrition labels. One thing that makes a lot of sense is ensuring you get your vitamins, and then keeping the rest of your food cheap. In other words, the most cost-effective food regarding calorie-per-dollar might be zebra cakes, but obviously you don't actually to just buy Zebra cakes. Living on black beans and rice might not sound appealing, but it is not the path to obesity. When you live on black beans and rice, other foods are your garnish. Sparing, small servings, but present from time to time. Most breakfast cereal is also effectively just grass seed + vitamin powder, as well.
[edit]
There was a time in my life where I had very little money, and I lived on black beans and rice for quite a while. I biked and walked around the city and I was thinner than I've ever been since.
People are often not aware of how their ability to function far exceeds some other people who are not so fortunate.
To describe a lifestyle of "surviving on black beans and rice" and riding your bike around, implies that you maintained a functioning household and kitchen with paid, active utilities; you were able to clean the room, vessels, appliances and utensils on a regular basis; you did pest control as necessary, and you were able to accomplish basic cooking tasks 2-3 times a day, every day.
Accomplishing all these tasks well enough to survive, feed yourself without hazard, and not become overrun with cockroaches is a sure sign of baseline mental capacity and cognitive function. Again, there are lots of poor people who were homeless, or grew up in dysfunctional households, or are on the brink of homelessness, and struggle with mental illness that militates against them "surviving on black beans and rice" day by day.
So I congratulate anyone who can accomplish these seemingly-trivial tasks. You deserve a pat on the back for sure!