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 correct: there are criminal violations if anyone puts anything in your mail box that is not US government approved “mail.”
This sounds plausible, but wouldn't work. The USPS has a history of defending its monopoly. Two example:
In 1971 a private corporation, the Independent Postal System of America, offered to deliver Christmas cards for five cents each — three cents less than the U.S.P.S. rate. They were stopped by a court injunction.
In 1966 the CF&I Steel Corporation, frustrated by the quality of postal service between their Denver headquarters and their plant in Pueblo, hired an armored-car service to deliver the mail. After five months of operation the service was halted by the Denver Post Office, and "at the Post Office’s suggestion" CF&I paid two thousand dollars toward back postage..
Someone should tell my Fedex driver, who has started doing everything possible to not deliver packages to my door. For the latest round the package ended up within my mailbox (which I didn't even think to check before calling in a missing package case). I'm pretty sure my mail carrier saw this when they delivered, and I don't think anything came of it.
