1. Safety: drones - multirotors, specifically - are very safe devices, inherently. They are incredibly simple (4-8 motors and no other moving parts). If they are dangerous, it's only because of lack of investment by the manufacturers to make mission critical hardware/software. That's the next step in the drone ecosystem though, as commercial use is gaining traction (multirotors are barely 6 years old now, IIRC. Mission critical flight systems haven't had time to develop). Furthermore, octocopters (8 motors, and there are variants with more) have built in redundancy (assuming a reasonably intelligent flight controller) against the loss of each motor.
2. Cost: An Amazon drone could be manufactured for few thousand dollars - $3k is the RETAIL COST of a DJI drone that can fly 10kg overall weight (drone, payload, batteries). That means at scale, and without retail margins, Amazon could make them for less than $10k, even if they are much larger and more sophisticated. The only wearable is the battery, and these can do many cycles (500+) before needing replacement, when properly managed. Other than that, the cost of maintenance are simply nonexistent.
3. Flight time: Simply irrelevant on an urban delivery service. An off the shelf commercial drone today can fly 10kg AUW for 20 minutes easily, lets say 12 minutes if flying at 40km/h - that means it has a range of 8km (and that's basing on simple off the shelf stuff, not purpose built and optimized systems). Manhattan is 3.7km wide and 21km long, meaning that with a handful of automated battery replacement hubs you can cover the its entire span.
4. Fleets and carrying weight: These drones will fly non stop, carrying up to 10kg at each payload. That covers 95% of the typical Amazon order and probably 99.5% of the things that you need just this second. The drones will fly non stop - I can't imagine needing more than a few dozens to cover a large city.
Bottom line: the technology is definitely within reach; I'd argue it's there, just needing some rich commercial entity to tie all parts together, test and certify. Nothing here awaits a scientific breakthrough to be made possible, and I'd say that technologically, it's easier (and probably safer) than self driving cars (which no one doubts).