Yes, the corner bodega is more expensive than the full grocery store, but they also probably have way lower sales per hour of labor, lower sales per square foot, lower sales per other overhead (rent, insurance, security, utilities, taxes), higher credit card interchange fees, higher shrinkage and spoilage, and pay more for their inbound groceries than the large chain down the street. If my guesses are true, all of these are perfectly legitimate business expenses and the corner store owner needs a return on their investment, just like the large chain does. (Grocers operate on razor-thin overall margins. Average net margin for the supermarket industry was 1.3%, 1.9%, and "1-2%" in the first three references I could find online.) Anything that increases costs basically HAS to go to the price as there's nothing else left to flex.
Payday jackholes can DiaF for all I care, but even the prevalence of those is driving in part by the banking regulations meant to "punish the banks" which have the effect of making poor communities "money losing to serve". When the predictable bank pullouts happen and payday lenders move in, it's not that hard to see the connection. Let the banks make a profit and they'll serve the community; prohibit them from making a profit and they won't, leaving only the even less savory financial businesses.