In Florida we have a turnpike run by a state owned corporation. It's very profitable.
As for the military, it would be profitable if we could charge for services, ethically. However, I would argue that it pays dividends in a different ways and you know it.
Edit reply: the post office is less useful in 2020 than it ever has been in its existence. It used to be an absolutely critical piece of infrastructure as people relied on mail for bills, communication, magazine subscriptions, etc. Now over 90% of mail is junk advertisements. People consume digital media, pay bills electronically, communicate electronically, sign documents electronically, etc. There is less and less demand for the parcel business.
I'm not arguing that we should shut it down, but the prices should go up and the USPS should be able to set prices without an act of Congress and it should be able to vary postage based on distance traveled.
My argument about the Florida corp running the turnpike is that it's entirely possible to run a state owned enterprise in a profitable way. The Florida turnpike is one of the best maintained with the best amenities of any road I've ever traveled on, including excellent beautiful rest areas and Tesla superchargers at every stop. Congestion is quickly delt with rapid construction of new lanes. The surfaces are kept smooth and free of potholes.