The Family Dollar has NO CASH BACK!! signs on every terminal because like Kroger they must have discovered razor thin margins aren't sufficient to cover transaction fees. For the same reason the city in the article may discover Dollar Tree has the same attitude about cash back transactions.
Short of government incentives there is no reason for a savings and loan to remain in a small unprofitable town and outside of North Dakota there are no government-owned banks. As much a it goes against the political climate these days you probably do need government regulation and incentives to keep banking accessible to these towns.
I use Ally Bank and they offer $10 reimbursement for ATM fees every month and they have a wide network of fee-free ATMs (at most 7-11s and a few other common stores). If you look harder, you can find accounts without any limits (e.g. Charles Schwab), and many credit unions support deposits in co-op ATMs (probably not helpful if there aren't any in rural towns). The only reason I go to banks is to withdraw cash in specific denominations for paying our baby sitter, but you can usually get the same thing if you ask nicely at a grocery store.
I don't see much of a reason why people need physical banks anymore. Withdrawals can happen with an ATM, deposits can happen in mobile or mail, and loans are increasingly available online. The only thing I can think of is business owners needing to make deposits and withdrawals frequently.