As someone who lives in a state with state-run liquor, this is the exact opposite of how it actually plays out. Prices are anywhere from 30-100+% more than across the border in a state without a state-run liquor policy. Because the government has a monopoly there is no competition to drive prices lower and since the government monopoly gets to keep the profit there is no incentive for them to lower prices. Furthermore, a big part of the reason that liquor is state-run where it is, with few, scattered stores that close at 7:00 PM and on Sunday and holidays, is to encourage reduced alcohol consumption. Raising prices is an effective mechanism for that too.

I think if you set up these kind of government-run dispensaries, you have to mandate that their purpose is ensuring product and supply chain quality (not just making fat bags of cash), and that revenue above COGS has to be restricted to what it costs to run the program and maybe a small emergency/maintenance fund. Otherwise the natural incentive that apply to any monopoly encourage them to raise prices to the max the market will bear and rent-seek. It's civically conscientious to think that the government would be advocating for the people by working to proved the lowest possible prices, but that isn't how any government-run 'vices' dispensary program I've ever seen plays out IRL.