It appears Amazon is in year 4 of a 5 year contract with the post office. I still find it odd that UPS would hand off the package in a metro area unless it was for special delivery. I live about 5 miles from both the UPS and post office facilities.
I would guess they save money doing it this way also. UPS used to charge more for residential delivery and this way they can deliver a load of packages to the local post office.