I'm reasonably sure that they are paid by the route, not by the hour, so if they want to screw around and take longer to get home its their problem.
Unfortunately that junk mail is what is keeping the post office alive. Even though USPS is supposedly an independent entity now, Clowngress still decides what goes on with them. The USPS could save boatloads of money by shutting down tiny post offices all over the country that could be served by larger offices, but to shut one down requires an act of Congress. They don't want to be accused of killing jobs by doing that, so they are sitting on their thumbs letting it fall apart.
The 6 day delivery week means that for every route they have 2 people assigned to a route, one that days 5 days and someone else that covers the 6th. That's a huge waste, cut it to 5 days and you need far less people so instant savings. Change it to a 3 day work week and that will just turn everything into a fight with the union, not really worth it when 5 day weeks keeps the full time employees going as normal.
I'm sure theres a lot of other streamlining they could be doing, if they weren't under the thumb of the government. The question is, do you allow them to make the cuts and transitions needed to survive on their own, or just allow them to go on as they are now but subsidize? The mail can't go away, at least not any time soon, and UPS and FedEx aren't set up for letter carrying to every single house like USPS does.