The only gotcha with the zip code reverse lookup is that there is a many to one relationship between city and zip. Look at Albany, NY (12201-12209) in the list you posted. There are a few with two cities, and iirc there are at least 3 other acceptable cities for 12203 that aren’t listed in that source.

My zip code maps to two different cities in two different counties. This causes endless problems with registering my car because the state wants to know what county my car is in and the webpage was programmed with the false assumption "every zip code exists entirely within one county."

USPS doesn't much care about counties. They assign postal routes based on geographical convenience, not political borders.

ON systems I work with, we run entire Street, City, State into Zip code lookup and compare with Zip code provided. If it's within postal code, we may present it to be corrected. If it's way off, we say "Umm, something is way off here, please try again." and flag it for fraud check.