Supporters of New Zealand remaining a constitutional monarchy, say that the status quo is fine. That unless you can point to a problem, why change.
I don't think the status quo works well, from a constitutional point of view. It doesn't work well, because it gives the PM far too much power.
In New Zealand the effective head of state is the Governor-general. The perform both the ceremonial roles, but also the constitutional roles such as appointing a Prime minister who has confidence of the House, approving an election etc. And while it is rare for the GG to have to use discretion, it is not unheard of. The most famous case being Sir John Kerr in Australia. But they have been used twice at state level in Australia. In canada two PMs have had GGs refuse requests leading them to resign. And in NZ we almost had the GG intervene in 1984 when Muldoon refused to act on the advice of the incoming PM.
In 1993 the GG appointed a committee of four people to advise her on who to appoint PM, as there was a hung Parliament. If Peter Tapsell had not become Speaker, she would have acted on the advise of this ad hoc committee,
So it is naive to think we will never have a situation where the GG has to use their reserve powers. And that is the problem with the status quo.
Who effectively appoints the GG? It isn't Parliament. It isn't even Cabinet. It is the PM, in his or her sole discretion. And the PM effectively has the power to sack the GG immediately. If Whitlam had realsed what Sir John Kerr was planning to do, and had got in first and advised the Queen to sack Kerr, she would have been obliged to do so.
It is somewhat mickey mouse to have the Head of Government unilaterally appoint (and be able to sack) the effective Head of State – whose job may require them to act independently if there is a question around the confidence of the House.
The King (weird to write that) can not intervene in a dispute between the GG and the PM. If asked to, he must back the incumbent PM by convention. If a GG refused a call by a PM to have an early election (as they have lost the confidence of the House), the PM could get the GG sacked and replaced within 24 hours.
So the status quo is somewhat broken. I want a system where the effective head of state can't be sacked at whim by the Prime Minister of the day. I want a system where Muldoon can't appoint a former National PM as GG and geoffrey palmer can't appoint a Labour Party Mayor as GG.
That system is simple. You have Parliament appoint the Head of State by a 75% super-majority. This will mean that you'll never get a politician again. The only people acceptable to a 75% super-majority of Parliament will be those who have distinguished themselves in areas outside politics.