USPS is only more "efficient" in certain areas of mail because the other players are legally prohibited from using the infrastructure: UPS and FedEx are not allowed to deliver non-urgent letters and may not use U.S. Mail boxes at residential and commercial destinations.
The USPS also has the benefit of being able to lose $7 billion per year and not go out of business, and I'd hardly say that is "efficiency".
How is any player supposed to compete against something like that?