It is extremely convenient when filling in online forms, giving an address over the phone, or when getting into a non-app taxi.
Web forms and the in-car navigation prompt first for the postcode, then present a list of the full addresses and you pick one.
Over the phone, "W10 6TR" also avoids needing to spell anything, and I encourage you to search Google for it.
There's also some human readable part. The W means West London, people who live in West or South West London will be familiar with some numbers - W10 is Ladbrook Grove. B is Birmingham, BS is Bristol, BT is Belfast etc.
Are you referring to the 5 or 9 digit variant? Presumably not the 11 digit one as that corresponds to your unique address. (It follows that the 9 digit variant corresponds to at most 100 mailboxes.)
I've never tried inputting my 11 digit code in an online form but at least the 9 digit one is readily accepted. In my experience the last 4 will usually be completed for me based on the street address and if it can't find a match it gives me an error.
I didn't even know there was an 11 digit code until now! I was referring to the 5 digit code. 9 digit would be closer, but around here 100 mailboxes (zip+4 would actually be 9999 mailboxes) is still quite a few square miles. If I look out my living room window, I can see maybe 10 houses, and that's with a view that comes from living on top of a hill.
