Let’s say I want to mail my car registration tax and fees check to the Box Butte County Treasurer’s office at the Courthouse. I do do this, incidentally, since it seems every time I go to the courthouse, the elevator in this 101-year-old building is not operational or the sheriff has access blocked for security reasons.
Since stairs are an ordeal for me, using the drop box actually makes sense. Going up isn’t the bad part. Coming down is as muscular weakness sets in, and I experience legs giving out…!

Yellow circle at bottom is mail drop box…; red circle is on the courthouse.
Wait! This isn’t hypothetical! This is what happens: I put my envelope in the drop box. If I beat the daily pick up deadline, it continues on its path to the courthouse that day. Otherwise, it sits there till the next day.
Once the envelope’s removed from the drop box, it goes inside the post office to be rerouted to the distribution center in North Platte, Nebraska, a 384 mile (618km) round trip by contract truck. While in North Platte, the envelope is sorted by address — a Post Office Box in this example — and re-rerouted to Alliance for distribution to that POB.
Someone from the courthouse stops by the post office to pick up the mail. The 384 mile round trip is for a piece of mail that needs to move 185 feet (113m) from a drop box south of the post office building to the courthouse in the next block north.

Alliance to North Platte and back: 384 miles round trip.
Seriously, for 49 cents worth of postage, I get to be outraged at the absurdity of a distribution system that counts a 384 mile round trip as the most efficient way to handle a piece of mail moving 185 feet from the drop box to an address a block away!
(Illustrations come from Google Earth.)