FEDEX would certainly try adopt the technology and compete if drone delivery looks like it is going to be the new wave ... I guess it would put a lot of people out of work though, you certainly would not need as much manpower if using drones to deliver packages... 
It would be cool I think, but you are talking about a hell of a lot of packages that get delivered everyday, especially around the holidays... that is a lot of drones flying around. The successful coordinating of an operation like this would certainly be a technological challenge.
LOL, there would be sooo many people loosing their packages within the first year or so of this taking off.
All new kinds of potential commute accidents and disasters as well. I would bet a whole paycheck that within the first year of this being practiced somebody would end up having a drone through their windshield or bedroom window.