I’m guessing the local governments wouldn’t interfere in the distribution process. The distributors would take the order, then deliver the goods to a government-run and government-subsidized food store.
At the store the looting would continue as before. That would hurt the city’s bottom line, but not the distributor. The distributor had better just require payment on delivery to the store’s location.
Hey, no worries, man! Just sue Tide and Colgate for making their products too attractive to thieves, right?