Please explain. Their high labor costs and lack of efficiency do not seem to meet this new low cost requirement.
I used to shoot with a bunch of USPS guys. If they have high labor costs I'd be amazed. These guys drive beat up vehicles, do not live in fancy houses, and are basically straight up middle middle-class. You might be thinking of the $85k/year figure I've seen tossed about but that's because Congress mandated that they pre-fund their pension fund in something crazy like 10 years. That's where the inflated labor costs are from. Guys that won't retire for 10-20 years have to have their pensions pre-funded. No private company would ever do something like that.
I'm about the last guy in the world to admit that the US government does something right, but the USPS is pretty good. Granted, the institution is older than the US itself. In fact it was instrumental in getting support for the revolution. When word of the Boston Massacre reached King George (months after it happened) he assumed the colonials would have barely heard of it. Unfortunately, for him, Franklin's post system had gotten word down to Georgia within 48 hours, and people were not happy to hear the news.
All that aside, when FedEx Ground was completely unable to deliver a package to my house (which is all of 6 miles from their depot) even after I gave them directions, I had to go pick up my package. A day later they sent me a post card, with my address written in hand on the front, asking for my address. Yeah, USPS got the post card to my house. Wasn't hard, since it had my address on it, but FedEx couldn't find the place.