Uber has announced food delivery in four cities. Uber is building self-driving cars. SpaceX has an autonomous spaceport drone ship. The FAA is (agonizingly slowly) creating rules for autonomous flying drones, while laws for self-driving cars are being handled at the State level. Rolls Royce is building an unmanned cargo ship. FedEx wants to build drone cargo aircraft to air-freight cargo from Asia. Drug smugglers are using unmanned submarines.
What do all these stories have to do with each other? It's that drones are bigger than just the aerial robots that hobbyists and the military use. This is a huge, tectonic change that is going to affect every part of our society that moves physical goods between two points. Amazon is leading in several categories (including inside their own warehouses) but there's so many possible use-cases it should be assumed there will be many niche players. Uber's food delivery service is just the tip of the iceberg.
I think a good mental model for the coming "moving atoms infrastructure" is the Internet. The Internet is a dumb pipe for moving bits over TCP/IP. Once drones because a sufficiently inter-connected network, it will essentially become a dumb pipe for moving packages. The centralized systems currently managed by FedEx and UPS will be replaced by decentralized systems that route packages just like routers treat packets.
This may seem like an unlikely scenario (who's the ARPANET in this scenario?), but I think it will become necessary. As drones take over moving more things, they will start to have to cooperate. UPS might not pick up at your location, so you hire an Uber to take your package to the nearest UPS store. Then there's a hand-off. How does that work? Uber and UPS will have to create a common protocol for exchanging payment, as well as shipping and handling instructions. This protocol gets adopted by others too (maybe Amazon and Wal*Mart use it to accept deliveries at their warehouses from UPS, FedEx, or a new competitor), and pretty soon you've got SMTP for boxes. Even if a company like Amazon wants to be the whole market, they can't. "Moving things" is too big for any one organization, so protocols of cooperation will be necessary.
And the fun part will be when someone creates "Tor for boxes", for ensuring privacy in shipping. There could be even be companies that "ensure discretion" by sending an unmarked drone (aerial or wheeled, depending on your needs) to your location for pick-up and then hand-off the box into the shipping network at a random location to hide it in the stream of commerce. The DEA will have a fun time with that one.