Government run shops let you track sales by area in a fine-grained way.
They can be a more effective way to ensure rules around supply are enforced than random inspections / checks.
They let you change the rules (eg opening hours, id requirements, record keeping, banned drinker registry, customer limits) easily without an outcry from retailers who would no doubt claim that any restrictions are onerous and impractical.
They can be placed so as to avoid completely saturating low income areas with booze.
No price wars or loss-leader marketing strategies.
They mean one can buy essentials without going "near" alcohol. Supermarket sales can be an issue for problem drinkers.
Retail profits can go back to the community.
There are other ways you can achieve each of these points of course but monitoring, enforcement and change will all tend to be more difficult in a decentralised vs centralised system.
I live in a state where restrictions on alcohol sales are pretty limited; grocery stores and corner/convenience stores, for example, can sell whatever they want alcohol-wise. Many stores will keep the more expensive stuff in locked cabinets as a shoplifting-prevention measure. I don't think it'd be too crazy to require that all hard liquors be kept that way, and then sales there can even be restricted by time of day if that was desirable. Beer and wine could be left as-is, with no restrictions. (On the downside, this would hurt smaller shops that aren't specifically liquor stores; locked cabinets are an added expense and take up more space.)