Just look at Walmart. They're dirt cheap because their costs and their margins are the lowest and consumers flock to their stores.
Funny enough, if you find the same products at other stores, they are the same price. I think Walmart thrives by offering a diverse selection of inexpensive offerings, not by pricing identical items lower (to reflect their lower workforce costs). For example, videogames cost the same at Walmart as they do at Target. To see a different price for a specific item, you have to go to a very different type of store (Sam's Club/Costco).
I think it's fair to say that even if Walmart could half their operating costs with technology, those savings would not find their way into the pockets of consumers.
Honestly, I think this is never going to actually be the case. Why would a grocery store lower prices just because their costs went down a bit? Neither the demand nor the supply has changed, nor has the price people are willing to pay for their groceries.
If nothing has changed but your costs, why lower the prices when you can simply report increased revenue to your shareholders? If competition comes along, a quick "we're premium, they are cheap" marketing campaign (or buying them out) would probably cost less than lowering the prices to match.