It happens, not as often as it is made out though. It is getting worse as there are a lot more part time and agency temps working now who don't really care where the mail goes. The management are just as bad. A large number of managers in this area were suspended for holding back mail and sending it out in vans when an audit was due so that the office complied with the clear office policy. Only one was sacked because he was found to have been nicking money.
Two of us spent three weeks tagging, bagging and inserting an apology letter into 60,000 items that a part timer had failed to deliver over the Christmas period. We, and the six posties who had to deliver it on the routes which he covered along with the normal mail, weren't particularly happy about that. His excuse was he didn't have time to deliver it as he had to pick his child up from nursery

He got let off with a caution.
They say the mail is less now. The stamped mail is, the ones with paid for stamps, the pre-paid and non stamped mail, junk mail mostly, has increased and the delivery times have gone up since they made it one delivery. They have also increased the number of delivery points to such an extent that it is near impossible to deliver all the mail in the time allocated. Complain and there is a witch hunt against the complainer 'till they find a way to sack him. That is from experience they tried it with me and a mate of mine but couldn't find anything. He became a trainer with the post office and I got new starts to train after that
To give you an idea of the job. On the run up to Christmas, especially the last couple of weeks, I could be delivering anything up to six bags with a total weight of 106 Kilos, no van and no bike. The bags were dropped of by the drivers at what was laughingly called second bag boxes or they met you somewhere on your delivery. I had 410 delivery points, flats, terraced houses and bungalows with long drives. Doesn't sound much but a normal day took nearly three hours to deliver, I still only had that time with the six bags. If I couldn't deliver a packet I had that to carry all the way round too. I'm not standing up for the new Royal Mail as I too think it is **** but it isn't all down to the posties.
I'm just glad I retired when I did