I'm sure it depends a bit on the delivery and sorting offices involved. The UK (I'm an ex-pat) seems to be WAY better than the US at this - it seems they really want to deliver the mail and make an effort to do so, vs here in the US where it's almost the opposite - like they are looking for any excuse NOT to deliver. I had one returned to sender since the post office wouldn't figure the missing town from the zip code…
This Tom Scott video shows some of the surprising (to me) lengths to which the USPS does go to figure out the right address: https://www.youtube.com/watch?v=XxCha4Kez9c Obviously this doesn't apply to your case, but I certainly didn't think they'd have a national center for decoding terrible handwriting.
It's cool how well integrated this is with the sorting centers where each mail piece actually is, so that the cases they handle essentially flow thru (with a retry attempt) as normal.
I've got to wonder why my piece with missing city but 100% legible otherwise-complete address including ZIP was still returned to sender. Seems it may have been policy for a certain class of mail (this was international registered, with a tracking number printed on it). In this case, to make matters worse, despite having themselves returned it to overseas sender, they then kept on sending me updates on their failure to locate it when I asked them to track it!