Earlier quoted context omitted.
The DMV loses money. The FDA loses money. The FCC loses money. These are public institutions, not for profit enterprises. They're funded partially by fees and usually largely by congressional appropriations. You beg the question by beginning by comparing the USPS to other carriers. It's one of the few public institutions required by the constitution! Even the Defense Department doesn't get that privilege, and it lose…
But should the USPS be a public institution? Many countries have opted to privatize their postal services, admittedly with varying results, but with quite a few successes as well: you may have heard the package division of what was once Deutsche Bundespost, now known worldwide as DHL. I do agree that right now is not a great time for radical changes though!
In those situations, their "competitors" largely just drop off their packages to USPS and let them handle the costly trip.