Yeah, most of the addresses where I grew up had no postcode of any description. Remember sticking forms of "munster", "mun" or "mun001" in there (the ones that validated it by UK Post code logic were the worst).
Later I moved to Dublin which had postcodes but they were more postal districts. So my postcode was "Dublin 8", which again was rejected by a lot of validators.
now we have eircodes so my postcode at that same address is d08 xxxx. We're getting on some sites the US style autofill of address based on Eircode as a result. but not everywhere's used to it. Just Eat, the largest takeaway ordering site goes sets my address to <house number>, <Street name>, <County Dublin>, but if I leave that as is, some local takeaways, including some very near to me see that as County Dublin as opposed to Dublin City and cancel the order thinking I'm out of delivery range, so I need to correct the final field to Dublin 8 anyway.