The wild thing is we could easily do this with a zip + 4 + 2, given each zip + 4 shouldn't route to more than two dozen addresses [1]. (Or 8 alphanumeric digits.)

[1] https://www.smarty.com/articles/zip-4-code

That's true, and it would be much easier to remember, but then you lose the feature where you move to somewhere else but you still use the same code - which is also a function of this system (you just update your address once, in that public database). And everyone who already have your digital id will automatically get your new delivery address, unlike if they just have your zip+4+2.