The only thing more inefficient than a purely governmental organization is a private company providing services to the government. There seems to be a persistent belief amonst citizens that governmental services would make them more efficient, more responsive to customers, etc, but following the money suggests different motivations.
The reason it is inefficient is because it provides services that a private company would not, or would charge a ton of money for. The USPS has to deliver mail to everyone with a postal address -- they do a whole lot of 'last mile' deliveries for FedEx and UPS, etc. Getting rid of the USPS means that a lot of people would either not get mail or pay out the nose for it.
Some things just aren't profitable, and frankly shouldn't be. Let's not forget that.
Seal Team Six Bake Sale! GoFundMe for Black Hawk nav system retrofitting! Reservists doing Speedo/Bikini carwashes! I'm sure it would work out great...