> There wasn't any easily downloadable file that had every ZIP code though
Post Service says what? https://postalpro.usps.com/ZIP_Locale_Detail (Heads up, it's Excel document)
I did not know you had a checksum in US zipcodes (I am French, oir zip codes are for the most part "region number"+"number that may tell about the importance of the city or carry a completely different meaning".
78000 is Versailles, which would make the city the "most important" city of the 78 "region", one of the ones around Paris.
78140 is another city, and 78142 (a mde up number) would be some internal numbering in the city, usually linked to a post office and usually unknown to the everyday Joe.
How this gets complicated is fascinating.
I know where I live what "city" you live in can be a complex situation because of unusual classifications of cities compared to the rest of the country so I can see this being a useful system to have.
We wouldn't have that problem in France where the cities are clearly separated. The concept of "city" (commune) is the basis for the topography classification of the country since 1789.
So when I input an address, a suggestion system will give me several choices with several distinct cities and zips. If I input a zip code, I can get several choices of "places" under one zip.
A situation where your address is in the neighbour city should not happen (I put "should" because this is France :))
USPS doesn't much care about counties. They assign postal routes based on geographical convenience, not political borders.