Since a majority of mail goes by air today, and you don't see any USPS planes, that could by why USPS contracts with UPS and FedEx.
Just think of the additional costs if USPS had to own and maintain their own fleet of planes and hire pilots and ground crews.
On a side note to current operations, I have some inside connections with the USPS system. Currently, they are handling far more packages than normal due to Covid online purchasing. With envelopes, USPS is handling that end fairly well, considering. With packages, they have warehouses and semi trailers loaded, but nobody to deliver the stuff to the area distribution hubs. UPS and FedEx are in similar situations, but they are set up better for package delivery and don't have to deal with letters.