That assumes the existence of a reliable, free postcode API of all addresses on the planet.

I did a very brief search, and none of the commercial offerings I could test recognised the postcode of the Eastern European neighbourhood I was born in. Also, like half of African countries don't have postcodes. It's just not a good system.

Only if you're limiting yourself tok those two countries. A lot of countries use the entirety of a 4 or 5 digit range for their codes. Any given 5 digit number is likely a valid ZIP code in at least half dozen countries.

The form stopped accepting input at five characters. I could not enter a "zip code" for my country even if I wanted to.

Even if they fixed that, there are other issues. (You pretty much need to cross-reference it with a database, which assumes said database even exists.)