It’ll work. Look at how many drones we’re flying around in the WOT. Most logistical problems can be solved by throwing money and people at it, Amazon has tons of the first and can get the second.
First problem with these drones is air rights. Currently the FAA requires aircraft to remain 1000 feet above ground over densely populated areas. To deliver packages with drones, you are going to have to fly much closer to the ground, and go over several peoples' properties. And I hate to sound like some hothead, but if one of those comes over my property, a shotgun or baseball bat will be used to remedy the intrusion on my property.
Someone delivering a package from the USPS/UPS/FedEx is not considered a trespasser when walking on sidewalks of neighbors to get to the delivery address. However, someone violating air rights with a drone will be trespassing on your property, and you have the right to take action deemed necessary to protect your property.