Amazon can (possibly) pull this off due to their scale and their warehouse technology. I think the other retailers that can be successful are those brick and mortar retailers with thousands of physical locations across the country (Walmart, Target, Staples, Kohl's)- imagine a reverse brick and mortar model where the customer orders from the site but it is fulfilled directly out of their local store.
The luxury apparel market is going to be the next wave of retailers who explore this offering and, could be, successful with it. Shoppers who are spending hundreds and thousands of dollars online expect an elevated level of customer service- same day delivery (like Net-a-Porter offers) is the next step in this personalized service.