It's not clear to me what the problem is that the article is outlining. The Dollar General near me has the exact same brands as you would find in any larger retail establishment, they just have found a way to stock the 80% that folks typically need. They are filling a niche between the gas station convenience store and traditional grocery/big box retail. They don't have a produce section, just a bit of fruit. Is that…
When dollar stores replace grocery stores in a community it reduces the quality of nutrition available. Potential vicious cycle there. Economic downturn --> worse nutrition -> decline in mental and physical health of community -> more downturn
Frozen produce - which the dollar stores in my area do carry - tends to be more nutritious nowadays. It is also much easier to prepare, and, assuming you have access to a freezer, is less susceptible to spoilage.
And if your food preparation options don't amount to much more than a microwave oven, or you simply don't have the time to do a lot of cooking, the frozen dinners that these types of stores sell might be one of the healthiest meal options you have.
Which isn't to say that food deserts are necessarily a good thing. I used to live in one and it was awful. But I do want to at least consider the possibility that the reason that these stores get a lot of business is that they are better serving the actual needs of their clientele. If that's the case, then perhaps the way forward is not to try and force everyone back to the old stores they probably did have a reason to not be shopping at anymore, so much as to try and figure out new things that suit their needs even better.