I suspect that buying a postcode is quite unusual. Certainly in Australia and South Africa, at least, postcodes cover quite large geographic regions -- a few thousands or tens of thousands of houses. According to Wikipedia, there's a postcode in AU for 100,000 people, and another for 22 towns!
An interesting question around vanity identifiers is whether it opens you up to attack -- if someone's tax file number, for example, is easily guessable, can that be parlayed into additional information and access by a bad actor? The current system is, I guess, just security by obscurity in that context. It actually makes me wonder whether there would be an opportunity around paying for a harder-to-guess identifier -- twelve digits instead of nine, for example.