Except everyone with a reliable car still drives to the large grocery store and with a wide selection which has lower prices and better selection on basics but makes it up with lower volume, high margin luxuries that the small market c doesn't have floor space for, and the small market, even if it starts as something else, ends up specializing in alcohol, tobacco, and dry goods, and neglecting general grocery items. Unless it's an area with a particular ethnic concentration and the small market survives by focussing on the unique demands of that ethnic community in a way that the larger store with a wider catchment area doesn't have any real incentive to.
Its not that there aren't enough small markets opened in areas of single-family homes to see this trend; you can't fix it with zoning, at least not in the manner you describe. (You can by driving density to transport capacity to the point where driving to the large grocery is impractical, of course, but that tends to be beyond allowing medium density, mixed use development.)