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You also made a good point - depending on where you live, getting access to these healthier items may be more difficult and I could see that also causing other issues, like transportation costs, etc.
It is definitely an issue as you get out further from urban centers, but I'm not entirely sold on the definition of what constitutes a food desert in modern times; for instance, in urban settings it is supposedly that a "substantial share of low-income residents live more than 1 mile from a supermarket or grocery store."
For my closest major city, the county I live in, and the county I frequent upstate, the numbers are:
Philadelphia, PA (100% urban) is 143ish square miles with 962 grocery stores, that is like 6ish per square mile on average.
Bucks County, PA (a mix of suburban and rural areas) is 622 square miles with 115 grocery stores, last time I looked, which averaged out to 1 grocery store per 18ish square miles.
Sullivan County, PA (100% rural) is 452 square miles with only 2 grocery stores
These are figures for full-blown grocery stores, not counting Dollar General type stores and whatnot.