Canada

in the middle? you mean the middle who also owns the start and the end supply of almost everything?

AFAIK the retail side in Canada is also making significant profits. Those could be removed or significantly reduced from the prices of a public grocery store. This would decrease prices in the short term. The oligopoly could then increase their distribution side profit margins, forcing the public stores to increase prices. This would make a very strong case for the comprehensive public solution that also tackles distribution. If you tackle just distribution, there's nothing discouraging the retail side of the oligopoly from cranking up their profit margins immediately. In effect, retail prices wouldn't increase, but the oligopolies would absorb the decreased distribution price difference. Then they'd get their politicians to say - see gov't wasted billions on this scheme and nothing changed, time to scrap the public distribution company. Ideally a public option should tackle both retail and distribution in one go in order to realize lower prices curbing the oligopoly's ability to prevent that via the distribution or retail sides.

E: I guess the oligopoly could instantly increase distribution margins in the first scenario too. Independent grocers would probably scream, but I don't know if that would be a significant impediment. I think it would be more difficult for the oligopoly to instantly stop any price decrease due to retail profit elimination, but I'm not certain lower prices would hold long enough for the public to take notice and oppose the inevitable calls for dismantling public distribution. So yeah, a public option would most likely have to have public distribution to succeed.

Ever heard of a co-op? They usually deal directly with the providers. No middlemen.

Seriously. Owning the logistics and distribution would do more, probably. And even then not for everything. You have to assume for anything manufactured the cost would get shifted around.

Frankly, the biggest difference I see around me is living in a place where the producers get direct access to customers AND where foot traffic is king. I've gone back and forth from rural to urban living spaces and here in the rural area I am now the big game changer is you walk up to a market and buy from fishmongers that bought fresh fish directly at auction and grocers that got a lot of the produce directly from the producer/farmer. And then there's enough people around in a small enough space that you can go to a supermarket for the packaged product and to a market/grocer for the fresh or specialty product.

The model where people drive to a shop and expect to find everything in the same place is a nightmare for pricing on both ends of things.