Those corner stores exist in a perfectly competitive market, they have low turnover so they have to charger higher prices to pay staff wages and rent. There are no abnormal profits. Why would you set up a government run store with more operational inefficiencies and less ability to respond to the local knowledge problem, than like give money or food stamps to people in these areas, or use the money in some other way?
There is no such thing as a perfectly competitive market. I don't understand why people on HN are obsessed with this term. It strictly cannot exist in the real world.
A perfectly competitive market requires the following (this is not everything, just some):
