The problem is criminality is so high in some areas that no amount of property tax relief will make up for shoplifting losses.
Its all water under the bridge anyway, as delivery services, amazon, etc, will make the concept of a supermarket as quaint as the concept of a record store or book store, in a couple years. I already get food delivered via amazon, I can't buy decent loose leaf tea locally or conveniently via any brick and mortar.
A true government operated store would resemble the DMV; wait in line for two hours to buy a bag of rice only to be told they only provide beans at this facility and you need to fill out another form and wait in line again. Then fill out the correct form and for homeland security reasons they can only provide the beans via mail delivery to your home address. And they can't give you beans until you give them proof of homeowners insurance and cooking training classes.