In the past, the receiver of a letter would have to pay the price of getting the letter. This system would get ditched really quickly.
Mail carriers would listen to what the receiver wanted and stop junk mail, when this became an issue.
These were the ideas I had in mind. I may post more but I wanted to see what anyone else had for ideas.
Take a look at the efficiency of UPS and Fedex, vs. that of the US postal service. The USPS goes around in tiny little cars, custom built for them, I think. UPS goes around in larger trucks that can carry more stuff. Private mail would probably run every day, none of this not on Sunday crap we have now. Also, we could have other companies all use the same mail box. Currently, it is illegal to use a mail box for anything over than gubmint mail. That’s why you have all those annoying newspaper boxes they put up all over the place.
I’m pretty sure UPS and Fedex don’t do Saturday delivery, whereas the USPS must deliver six days a week. The mail vans you speak of ARE custom designed, but they’re also the only legal right-hand drive vehicle I know of(they were also designed to be fuel efficient); USPS is also moving to fewer routes serviced by larger vans. Also, remember that the Postal Service only has a monopoly on nonemergency letters - it competes with private companies to deliver packages(using its universal service mandate as a selling point) and until very recently actually turned a profit(when it did, most of its costs were labor-related).
In other words, the private market would deliver mail a lot less often - even the postmaster general’s asking for 5 days-a-week deliveries.