You're right that "people can't afford healthy food," but not in the way you think. The less that is done to a food, the cheaper it is. That's why boneless chicken thighs are more expensive than bone-in legs, and the fried version even more so. Grains, veggies, whole fruits, etc, are much cheaper than sugared cereals, fruit juices, and prepackaged meals. The New York Times did a comparison several years ago that came to this point.

However, because less has been done to the food, you have to spend more time cooking it. And time is exactly what most low-income people don't have enough of. Time is the most costly ingredient in making healthy meals, and paradoxically, the more money you have the more time you can buy. You also have to buy smaller quantities of fresh food more frequently, rather than a large quantity of packaged or processed food that will keep for longer. Given that American cities are designed such that you can't just walk to the store to pick up what you need, but must instead drive and spend time in traffic just to go get groceries, people (especially those struggling with their finances) are incentivized to make fewer grocery trips, and thus to seek out the packaged and processed foods that allow them to do so.