Anecdotally, I'm getting my neighbors mail several times a month. I can only speculate about how much of my mail gets delivered elsewhere.
Privatizing the mail doesn't magically prevent delivery mistakes from happening, despite what you appear to be suggesting.
For business customers, accepting a package and failing to deliver for the holidays is WORSE than accepting (a la USPS) with no limits and then having it get stuck.
UPS did this to amazon once, and that was enough for Amazon to decide to build out its own delivery network.
Shippers can do all sorts of things to help make things efficient if UPS communicates the limits. Ie, no sales with guaranteed 2 day shipping 2 days before xmass.
How can you say for certainty that they won't do it again? Are you in a leadership position at UPS where you're able to make that assertion?
https://en.wikipedia.org/wiki/Informed_Delivery
https://informeddelivery.usps.com/box/pages/intro/start.acti...
The USPS already scans the exterior of every letter they deliver (perhaps a result of the 2001 anthrax attacks?). They let you see the scans online. You don't have to "speculate" about losing mail.
The privacy implications suck, but c'est la vie.