In practical terms I cannot stop having a mailbox, because a few times a year a check or something comes in the mail. That means I would have to go get my mail from the post office every so often and go through it all. So all that's accomplished is I have to drive a few miles down the road to pick up my USPS garbage instead of having the garbage delivered into my front yard. If the USPS didn't exist at all, everyone (businesses, official government notifications, etc) would switch to the better service providers like UPS/FedEx.
http://www.costhowmuch.com/ps/fedex-letter.htm
Of course, that comes with a guaranteed delivery date, insurance, tracking, etc. I'm sure the private carriers would charge more than the USPS if they were servicing the lowest end mail, but currently the USPS is monopolizing that.
Also important to note that the USPS is subsidized by the spam they deliver which primarily winds up in the landfill. If the USPS wasn't filling everyone's garbage bin with bulk rubbish every day, their clearing price would be closer to private shippers. To put a scale on that, I have one trash can in my house that is at my desk and only winds up getting garbage mail tossed in it. Every two weeks I have a 13 gallon garbage bag full of mail garbage. What is the time-cost of every household in my city dealing with that much extra junk? What is the environmental cost?
Raising the lowest price for sending junk mail to the prices of UPSFedex would certainly reduce spam, but this has nothing to do with how the services are governed.
FWIW it appears you're free to individually act on your desire: https://www.quora.com/U-S-Postal-Service-Do-I-legally-have-t...