Apples and Oranges
It makes no sense to compare the USPO to FedEx. They're in completely different industries.
FedEx specializes in rapid delivery of packages and time sensitive letters.
The Post Office offers these services, but they're main product is delivery of small, non-time sensitive material at incredibly small prices (and yet Americans still bitch about 3 cent price increases) and with almost universal coverage (the post office maintains a large number of 'branches' that are ultimately unprofitable, but they're mission is to provide postal service to everyone in the United States).
One reason that the Post Office is quasi governmental is because the ability to communicate via post is seen as something of an entitlement. As a country, we do not want to end up with some large percentage of the rural population cut off from post service for profit reasons.
I send out over 4000 pieces of first class mail every month at less than $.35 per piece. For my $.35 cents I get reasonable delivery time (95% within a week), returns on failed deliveries (95% within a month) and address correction service. If we suppose (rather simplistically) that the post office gets a 33% break by not paying taxes, I still don't think any private delivery firm could offer that service at $.50 per piece. (Nor would they be interested).
And for the record, I use FedEx a lot for package service, but they end up screwing up my delivery a good 10% of the time (UPS is far worse). If you really want a good delivery company, use Airground Express.