I can’t speak exactly for NZ but I assume it’s similar to Australia; it is normal to get charged a discharge fee from the bank your leaving and there maybe an establishment fee at the bank your refinancing with, along with another small cost to change the official register of state government. This could all amount to a couple of thousand dollars every time you refinance.

We do have ARMs in the US, but fixed mortgages are a lot more popular - presumably because they allow someone to know how much it's going to cost.