Improbable things happen frequently at scale. One possible scenario is just that this card got lost twice.
It could have slipped behind a counter at the original post office and been uncovered when that office was decommissioned 35 years later. Then it would have made its way to a newer sorting facility where either it could have been misplaced again or, more likely, been stuffed in a cabinet somewhere (as I doubt USPS was as adamant about delivering lost mail in the 1950's). That facility could easily be in operation until today - or decommissioned very recently.
No idea if anything like this actually occurred. But at 400M+ letters / day, USPS has the scale for unusual circumstances like this to be somewhat regular occurrences.
To some degree, I'm sure it was a plot device but 19th century English novels often depended on rapid/same-day communications via letter at least in the environs of London.
Probably a reason. Also a lot of middle/upper class people were leaving cities in the US.
Bike messenger services also were a big thing in cities a few decades ago. Email (and probably general acceptance of electronic scans) replaced a lot of shuffling around of paper documents. I was sort of amused a month or so back, when I had to do some financial transfers, a lot of the paperwork that would have formerly involved going into an office and getting notarized stamps could now happen with a combination of a phone call, mailed paperwork, and phone verification.
It could have slipped behind a counter at the original post office and been uncovered when that office was decommissioned 35 years later. Then it would have made its way to a newer sorting facility where either it could have been misplaced again or, more likely, been stuffed in a cabinet somewhere (as I doubt USPS was as adamant about delivering lost mail in the 1950's). That facility could easily be in operation until today - or decommissioned very recently.
No idea if anything like this actually occurred. But at 400M+ letters / day, USPS has the scale for unusual circumstances like this to be somewhat regular occurrences.