This article suggests there are many drone capable of transporting 40lbs, or more. I agree that drone delivery is not ideal for every situation, but I can see many use cases. For a typical suburban neighborhood, with 1/4 to 1/2 acre lots, a delivery truck could park in a fairly central spot, then deploy 8 or 10 drones. A single drone could carry 2-3 packages, and make those deliveries in less than 10 minutes, following the neighborhood streets so as to not fly over anyone's house or property. Heavier packages could be handled by the truck driver, while the drones are off working. This might scale even better for a denser urban settings.
The article suggests that this is a management problem, rather then a technical one. I cannot speak to if it would save any money, but at Amazon's volume I can see why they are so interested in this a means for delivery.