The USPS gets a monopoly on its gigantic market from the government. That is an enormous government subsidy. It is very much not like any other business.
The USPS does have a special relationship, but it isn't a one way street. First, it isn't a monopoly -- there are many other shippers competing in the profitable segments of the market. Second, USPS is obligated to service every location in the US, and at government-controlled prices.
USPS will deliver, door to door, a letter from Nowhere, MT to Remote, GA for $0.55, even though they take a loss on it. Try to get Fedex to match that.
Perhaps you should look at USPS Publication 542, https://about.usps.com/publications/pub542/welcome.htm, which describes how they have a monopoly and the power to levy what amounts to a tax on anyone that competes in a prohibited way.
But it is. A simple googling gives many hits confirming this simple fact. This one seemed most informative:
> The USPS actually has two legally enforced monopolies, as per Title 39 of the US Code. One is over the delivery of anything defined as a “letter,” which is within certain size and weight limits. The second is over the use of your mailbox.
That is defining monopoly in a very constrained way. You might as well be complaining that USPS having a monopoly over delivering watch fobs. FedEx isn't trying to capture the $0.55 letter delivery market.