It's not quite that simple. A NZ citizen needs to be resident in Australia for a period of time before applying for Australian citizenship. But it is certainly a lot easier than many other countries.
https://immi.homeaffairs.gov.au/entering-and-leaving-austral...
You can work freely and get access to Medicare (and vice-versa) so they’re more-or-less citizens anyway.
And another feature of the system: if an Australian has any connection to NZ or knows where NZ is located, they’ll be deported to NZ if they turn out to be a criminal.