I'm not sure where you got that idea, they are specifically listed as prohibited in multiple places, including the Google search preview card.
That said, the only real punishment is the lack of any compensation if it gets lost.
I got that from the Prohibited Items list, which doesn't contain currency: https://www.nzpost.co.nz/personal/sending-within-nz/prohibited-restricted-items
The great news (lol) is that the Postal User's Guide does not actually agree with that page, and forbids it: https://www.nzpost.co.nz/sites/nz/files/uploads/shared/APA2020/postal-users-guide-2020.pdf
Consistency is overrated.
Fun fact, you aren't allowed to send Prezzy cards or JB Hi Fi vouchers either - gift cards are a prohibited item.
Eva888: I also looked on the DHL site and they specifically mention local money prohibited. As long as it’s just at my risk and I won’t be arrested because its a crime :)