I can't think of many pro's to becoming a republic
I can think of one but it is so important that it is clear to me that we should become a republic.
When a head of state visits another country, they get treated as you would expect for a head of state.
They meet the top figures from the state that they are visiting - bankers, business leaders, government ministers etc etc.
They will in be accompanied by people holding similar roles in their own country.
The visit will facilitate meetings between those groups from both countries.
When the British monarch visits other countries, they are not accompanied by the head of federated farmers or the New Zealand minister for trade or anyone else representing New Zealand interests.
When our Govenor General visits another country they are seen as a miinor official and they do not open doors in the same way.
We are losing out because of this and we are conducting the promotion of New Zealand's national interests with one hand tied behind our back.
It costs us in trade deals, influence, investment and I expect many other areas.
Maybe not when our Governor General vistis other countries (does our GG do State visits?)
But certainly, when our Prime Minister visits other countries, all those things you mentioned happen.
For all intents and purposes, for diplomatic visits, our Prime Minister IS the head of state.