I must be missing something here, because I can't see any reason for a store to turn this down. They're getting a free inventory system, and they're being shown in local search results. The alternative is to pay for an inventory, and never have a chance to win the local search customers at all.
Sure, some customers will go to Walmart instead of a locally owned business, but how does the local business benefit from not being in the search at all?
If there are 4 stores in the "local search" and you search for "DVD Player" and each of the 4 stores lists "DVD Player X" and 2 have it for $100, 1 has it for $120 and 1 has it for $80, where do you go? You go to the $80.
As I explained in other comments, people currently shop based on expected value, they can't know for sure that shop x has the best pricing but they have been there before and got a good deal so they assume it will again provide them with a good deal.
If the only concern when purchasing is "which has the lowest cost?" this app would mean that EVERY user of the app can have that question answered, currently in the real world the question is "does the potential saving justify the time investment of visiting every shop and finding out their pricing"?
If there are 4 stores in the local area and you've previously bought a DVD player from store #2 for $100 and you want to buy another and you think $100 is around the best price you'll find you go to that store and purchase it; sure you didn't get the best price but was the POTENTIAL SAVING (which is entirely theoretical) worth the time investment to search out by visiting every store?
This app would create a race to the bottom, it would be worse than online for retailers because shops are quite close together, the only "cost" to the customer is the effort required to get to the cheapest store, in any mall or shopping district that's probably a very short walk. With online stores you can compete on shipping, next day vs. 7 days even though the item costs $5 more? I'll take next day, but $5 more to save me walking 20 yards? Not going to happen.
Local search would be great if you're the lowest cost retailer, otherwise it'd be a big problem.
Sure, some customers will go to Walmart instead of a locally owned business, but how does the local business benefit from not being in the search at all?