Price gouging has been a major problem at Canadian grocers since COVID. Basically prices went up with supply chain issues / inflation but have not been adjusted for improvements in inflation since then.
These are for profit entities. They would steal a quarter from the poor and hungry if they could.
That's the fundamental flaw to capitalism - not that it concentrates wealth and power (because that is perhaps human nature) but that it celebrates it.
It conditions us to think that concentrating wealth is not only morally right but something we should all aspire to. That competing is morally superior to sharing.
Ultimately, if capitalists accrue so much wealth and power that they can buy out the interests that would seek to regulate them through democratic will, we then relinquish our democracy for feudalism.
I think the problem is that the antitrust ship has already sailed.
I don't think a government run grocery store would be looking to compete on the open market. It would be more along the lines of subsidized food for lower income households on food stamps, practically speaking. That is much more sutainable than one that's open to the general public.
If a government run grocery store could provide a fair price for items we are currently being gouged on, I doubt they would be able to keep up with consumer demand. Essentially middle class and above will have to keep putting up with commercial prices.