I'm not so sure. UPS drivers are unionized, and work rigid routes and hours. They also must go to many places to just pick up items. Amazon delivery drivers would have none of that.
There has been an Amazon delivery service in our subdivision for a couple of years that has a non uniformed driver, driving around in a non licensed golf cart type vehicle. It is part time, fast, maneuverable, and appears to me to be quite efficient. UPS couldn't touch its cost.
It seems that Amazon is trying everything they can think of to streamline delivery. One problem is almost everybody wants next-day delivery. I don't have Amazon Prime. Because I'm willing to wait a few days for delivery, it's free.