Note that they don't have to be a monopoly to cause a problem. Usually the way things go is these state-run grocery stores get subsidies. The goal is to provide food in food deserts, not to be profitable. Over time the subsidy inevitably grows meaning higher taxes for non-gov grocery stores. This leads to a cycle where the state-run stores pushes out the corp-run stores with the thinnest margins.

Ultimately only the bougie grocery stores remain in rich neighborhoods and now you have to really hope that you can continue funding those state-run stores or you just made the food desert problem a whole lot worse.