There are areas of the country that actually are healthy food deserts.
Local food retail stores can influence what food the local population buys and consumes. It takes more management and equipment to offer a good selection of things like fresh produce than it does to offer processed foods in bags or cans.
People receiving SNAP benefits are less likely to travel a great distance in a car to get a better selection of healthy food than their local mini-mart or gas station offer. And that is if they have access to a car to travel.
The time and energy cost to prepare food must be considered. People value convenience and consider bang for the buck when purchasing food to satiate their hunger. Ready to eat calorie dense foods containing a high percentage of fat fill people up quickly and relatively inexpensively. Yes you can buy lots of healthy rice and beans for $13, but then you need to spend a lot of time cooking those before you can eat them.
Some Medicare Advantage plans provide certain amounts of monthly $ credit on a card that can be used to purchase food. But only certain foods considered "healthy" can be purchased. Candy, ice cream, cookies, soda, many processed snack foods can't be purchased. For example most cookies can't be purchased, but granola cereal (some of which contains more sugar and fat than the cookies) can be purchased.