I used to live in a small Minnesota town and the only liquor store was run by the city. The prices were reasonable for how rural we were, and apparently some of the profits helped with city expenses. However, there was a grocery store 15 years ago or so that apparently wanted to open in the town and also have it’s own liquor store, but the town denied their permits for the liquor store for officially unclear reasons, lol.
Getting someone else to buy it isn’t actually the only way kids get it in states with really loose liquor laws - when I was a teen, I heard of a few places, mostly gas stations, that never carded. Eventually they got busted by the cops, but they sold a lot of booze to my friends before that happened. I don’t think that’s justification for exclusively state run liquor stores though. But I bet the people working at government run stores get better benefits and more stable hours than the ones working for private businesses…