* Regulations. e.g. commercial drones in the U.S. have to be "piloted". Fully autonomous drones are disallowed.
* The need for an infrastructure: you need to have a large network of charging / refueling stations, and also warehouses set up for drone delivery, in order for there to be a large drone delivery presence in the U.S. This can be compared with the difficulties faced by electric cars -- you need a network of charging stations, in order to compete with cars that use gas stations.
I don't think the technology limitations, and need for extreme safety, are where the holdup is. I think they basically have the technology; and are just waiting for regulations and infrastructure to be taken care of. The infrastructure will take some time, and will probably be built up region-by-region -- so will take several years. The regulations could, in principle, be cleaned-up tomorrow, if the government allowed; but, given how slowly government moves, it may take a couple more years.
Incidentally, Amazon has been really secretive about their drone program, even giving their employees fake ID names:
At last year's internal all-hands meeting, Bezos was asked by an employee when he expected to see Amazon packages delivered by drones, according to a recording of the meeting obtained by Business Insider.
For the answer, Bezos turned to Jeff Wilke, the retail chief who at the time was in charge of Prime Air, after saying, with a long, emphatic laugh, "By the way, I might have submitted this question."
Wilke said he didn't have anything to share, only adding to say that he's "optimistic" as the team is "working hard on the regulatory and technology constraints in parallel."
As Wilke started to walk off stage, Bezos followed up with a frowning expression.
It's possible that the "infrastructure" part could be sidestepped using extreme long-distance drones. They exist. For example, here is a company that makes drones that have a 350 mile range:
The VOLY M20 is a new generation of dual role aircraft offering customers the ability to simultaneously carry 20 pounds of cargo and a 10 pound ISR or sensor payload. It was designed to meet the exacting requirements of commercial customers operating in remote maritime locations and military customers who require a flexible vehicle for resupply and ISR applications. The VOLY M20 has a 350-mile range, cruising at 75 mph, and more than eight hours of endurance for sensor operations.
That would also be useful for shipping medical supplies to hard-to-reach locations from far away -- e.g. during a blizzard, when roads are iced-over; or following a hurricane that downs trees and power lines, blocking roads.