I highly doubt that a consumer would see any financial benefit from this. Sure different grocery stores use different products as loss leaders, but the trade off is time, so rather than the cost of having one person go to one store and by X number of items, we're sending either one person to three stores for ~X/3 items, or three separate people to three stores. All of which will take more total time than 1 store, which puts more resource demand and will cost more to the consumer.

Also, it would rather be in the faceless ai shop's interest to arbitrage orders, always show the "middle" price but use the cheapest one for orders.