I used to organize activities like block parties in my neighborhood, and to inform people about these events I ran off a flyer for them to hang on their refrigerator, and it included my phone number if they wanted to talk to someone about it. Once I got a call from the postmaster of the town telling me that if they found another flyer from me in someone’s mailbox I would be in trouble. So yes, USPS has a monopoly on putting anything in someone’s privately purchased mailbox unless it’s got a cancelled stamp on it. So I could not even hand deliver this information without taping it to a door.

And you are right about postal rates being established by the government, but it’s not by Congress but by the Postal Regulatory Commission, which is appointed by the President and approved by the Senate. So a bunch of political appointees determine the cost of sending a letter or package rather than the market. It’s not efficient, and thus you have made another argument against having the government do mail delivery.