Could the private sector more efficiently run USPS?

Of course, so long as by "efficiently" you mean slashing worker's pay, getting rid of pensions, and not delivering mail to rural areas.

Capitalist economists using "efficiency" more or less interchangeably with "profitable" has melted so many brains. There is nothing more efficient about the shareholders sucking up more money by ripping off workers and customers.

Industries will get privatized and the only thing they do is stop providing the service to poor people and pay their workers less, and this will increase "efficiency".

What this has to do with the normal use of the word "efficiently" is anyone's guess.