I think in general people in this thread are missing an interesting facet of this solution. Suppose that the inventory system was also a POS system (which it'd probably have to be in reality), there's opportunity there for lots of analytics that a brick and mortar store just doesn't get. And, there's even the opportunity of integrating deals for loyal customers, etc, etc.
The company providing the service could also get access to shopping records of individuals at various brick and mortars--something that probably doesn't exist, which could lead to targeted advertising on receipts (which the shop owners could take a cut of, for instance). There's lots of ways that all parties involved could benefit without killing the small businesses.
The system behind the app should be both. When you think of yet another groupon, you jump a little to short IMHO. But if you add POS, inventory management and a unified sales / distribution channel and provide that to local stores and shops you'l get quite a product.
But can't I stop to think of pg's frightening ambitious start-up ideas here? The odds are certainly against you, but the rewards will be equal if manage to pull that one of.
POS systems are complex and need to have very low latency. On top of that, there are many different types of registers that can be used. On top of that, since you are dealing with the everyday transactions of a business, in order to ship your product you need to be damn sure it works as expected. This is going to lead to very long and expensive development times.
The investment for the stores that would likely be excited to be apart of this is too high for those stores. That software isn't free when they need to get new hardware to support all of the systems that need to integrated so that they can be apart of the search.
No one says that this has to be a GroupOn play. CVS (the drugstore) has a loyalty program in which they give money back (in coupons) for money you spend. That sort of thing is certainly possible, and probably works fairly well.
The company providing the service could also get access to shopping records of individuals at various brick and mortars--something that probably doesn't exist, which could lead to targeted advertising on receipts (which the shop owners could take a cut of, for instance). There's lots of ways that all parties involved could benefit without killing the small businesses.