Why would you buy Whole Foods to compete with Walmart? Seems like totally different branding and target markets...
What if Whole Food's brand cachet means as much, or more, to people who can't afford to shop there? In some circles 'Whole Foods shopper' is a denigration, drenched in jealousy. There may be a demographic that perceive Whole Food brand aspirationally, who will be brought in by reducing quality and prices.