"The healthcare system of New Zealand has undergone significant changes throughout the past several decades. From an essentially fully public system based on the Social Security Act 1938, reforms have introduced market and health insurance elements primarily since the 1980s, creating a mixed public-private system for delivering healthcare."
I don't see what this has to do here, since the other comment was comparing to Portugal, Spain, France and the likes.
In any case, usually when you start making it private it gets better for a little while, to convince people to move over, and the government to defund the public one.
Then when the competition from the state is over they can start reaping the profits (like in USA).