The food deserts thing gets tired. It's a social media trope at this point. I lived in poorer neighborhoods growing up, and those who wanted to eat healthy made it happen. It just took more work, which is the point. Corner stores that stocked fresh fruits and veggies would just have them rot on the shelves due to no one purchasing them. It's consumer preference.
Almost nowhere in the US walks to go to the grocery store. Exceedingly small portions of major cities. Where I live in Chicago is quite walkable, but the vast majority of my neighbors load up the car for the vast majority of their shopping trips. There are pockets of course, but they are rare.
My neighborhood also happens to be much more fit than the national average - obesity is somewhat rare to see. The correlation is with wealth. Why there is such a correlation is much more interesting, and it likely is not as simple as people want to believe.
Same goes for the poor inner ring suburbs where I lived in my 20's in a different state. Very high rates of obesity. In the rich outer suburbs obesity levels were visibly less.
It's far cheaper to meal prep and make your own food from base ingredients. It doesn't need to be fancy. When I grew up poor (working class) this is how we made it work. By buying staples in bulk and buying other items opportunistically on sale. We didn't even own a car for most of that time - and the nearest grocery store was at least 3 miles away. It simply wasn't an option to exist off of junk food since it was too expensive.
Eating junk is easier and more convenient. It feels good in the immediate moment and is low-effort. It's the default, and the environment around you encourages it. Add in lack of any peer pressure and it being normalized by those around you and I believe that explains nearly everything. Lack of walkability certainly hurts, but it's not a primary driver anywhere I've lived.