Well, I think this is a scheme to make people think the post office works better than it does.
Hmm, my Netflix movies, the ones that I put in the blue box Sunday, to be picked up Monday by 7am, didn't clear Netflix until 4pm on Tuesday, which is later than any other time I've ever seen them clear. That could be because of X-Mas of course, but it definitely didn't get sorted and delivered any earlier than when I dropped off movies in mailboxes marked 3:15PM pickup, or even when I went inside the Post Office drop-off slot right before 7PM (might have been 6:30PM, can't remember for sure).

So the point it, drop letters off in any mailbox before that day's pickup time and your mail will get to where its going same time.

So my only question is, why even post the pickup times?
Just list the latest pickup time, and give the Post Office the flexibility to adjust multiple intra-day pickup times based on trends and historical data.
Or does that make too much sense and that alone would be a good enough reason for the government agency not to do it?