They remind me of Social Security numbers in a way, where an identifier created for one narrow use (internal Social Security use only) ended up becoming a de facto standard (national identification number) due to the absense of a suitable alternative.
If you'd like to go further down the ZIP code rabbit hole, a few interesting codes to research are `00501`, `48222`, and `12345`. :)
I used to love leaving that site open on public PCs and watching the reactions that resulted :)