Oh believe me. If that parent company was dumb enough to remove prices from items, and if that is even legal in your state, then a competitor would enter very quickly, making a big deal advertising about how it displays prices, and everyone would start doing their shopping at that competing mid-tier grocery store. Because that's how capitalism works.

You are making the fundamental mistake of thinking that the current equilibrium of local stores will continue to persist once some of the stores make a deep and fundamental change to their business. That is obviously not the case. It would create a gigantic strategic opportunity for competitors. And competitors really like finding strategic opportunities where they can make a bunch of money now where they couldn't before.