We still deliver on Saturdays, in most places. Yes, I work for the Postal Service, since 1998. I have worked on those very machines that sort the mail for carriers(DBCS- Delivery BarCode Sorter), and while they do on occasion make mistakes, they also get more done than the old days of hand sorting everything. But I will agree with most of everything else you said.
This storyline is one of my favorites. Still brings tears to my eyes. :’(