If FedEx and Amazon set up private airports dedicated to these machines, only put cargo in them, and make their flight routes distinct from other aircraft, I imagine this could be up and running faster than people think. Edge cases shouldn’t result in loss of life, so getting through regulations and insuring should be much easier than other situations.
Don't forget that aircraft falls on someone or someone's property.
To be fair, maintaining straight and level flight— i.e., not falling out of the sky— is the easiest part of flying an airplane. Computers have been good at that for a while; in fact, that’s how airline flights are controlled these days during basically all of cruise flight (by autopilot).
Takeoff and landing are the tricky parts.
(I say this as someone who’s firmly on the skeptical side of the spectrum regarding the near-term prospects for fully autonomous vehicle control.)