Canada

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.