You can't have food that is at the same time cheap, healthy and at your doorstep. You can have two of them. Walmart gets you cheap and nearby. If you want healthy and nearby, go to Whole Foods and be prepared to stretch your wallet. Not everyone can afford it though.
I don't think the stores that used to exist had the same or superior choice of goods and the same prices as Walmart did. I mean there might be some that did, but they persist even in the presence of Walmart - I have several Walmarts within 15 min drive of me, and still know a bunch of local grocery stores and specialized shops that still do fine. But I am not sure why "local store" is inherently superior to Walmart unless it does something better, or how it will be able to deliver on the all three.