The eVisitor 'visa' for Australia is free, so even if NZ needed to cover their levy with an ETA, they could have made it free. But, they didn't...
I haven't been interested in visiting Australia and New Zealand for a very long time, but my partner wants to go there (and Oz, where I have to pay a $20 service charge for the ETA, as I'm not eligible for the eVisitor thing (partner and kids can get the eVisitor) - no idea why one has a service charge and the other doesn't...).