That's a bit of an apples and oranges comparison. The thing about for-profit prescriptions is that they incentivize doctors to prescribe opiates for people who don't need them, people who may not have even been interested in them. A for-profit retailer selling alcohol doesn't have that aspect at play at all; at most the for-profit aspect encourages flashy advertising and displaying alcohol more prominently, but nothing to the level of having a trusted expert in a one-on-one setting personally pushing for you to consume.

Instead the pressure to consume alcohol comes at a grassroots level. Social alcohol consumption is deeply rooted in human culture, and it's generally the people around you who will push you to consume. This pressure is independent of any profit motive, so removing the profit motive does nothing to affect it.

> AFAIK rates of alcoholism aren't even different between state-run and private sector models

Looking at some 2016 WHO statistics, the US seems to have ~3x the rate of alcholism as Iceland, but I recognise these are cherrypicked examples and I'm not interested enough to do a deep dive aggregating countries. Still, it seems plausible that government intervention can reduce alcholism rates. The fact that it's not 0% means nothing; nothing in the world is 0%, outlawing murder doesn't mean murder doesn't happen, but you can strive to reduce it as much as reasonably possible.