Again a big piece of this is because food deserts don't have fresh food, so you have to commute to shop often.
Tbh I am skeptic of the whole narrative. Maybe the poor tend to lack education, including knowledge about healthy foods.
Because they don't have as much money as other areas so people follow the money with where they provide services
>tend to lack education, including knowledge about healthy foods
This is also true and again structural - see above. Poor areas don't get school funding because school funding is based on county property taxes and thus, do more poorly than rich areas
It literally all boils down to structural inequality
And even bad schools could find a minute to tell kids they should eat more veggies and less sugar?
Having lived in these areas for most of my life I can tell you it's often only specific low quality chains (Church's, Grannys, Jack in the Box etc...) or these "chicken wing/chinese food" shops that basically just fry up the worst meat and slather it in sugar sauce.
I recall in high school, peers of mine would simply eat a bag of Doritos for lunch - as even the classes like Home-economics were largely just holding cells for teenagers until graduation.