An Australian build would be too expensive for an export order, we could not compete with an Eastern Euro or ROK shipyard building the A140 or any other Euro or ROK design. Australia gets economic and Tax benefits, by building RAN ships in Australian Shipyards, NZ would be paying full price with zero economic benefits.
It is not particularly in Australia's interest to make profitable ships for NZ. I don't think that would be a concern, if NZ wanted something that Australia was building, we would bend over backwards to accommodate them, including on price. If they really wanted to work and be in with AU on ships.
With the Pacific Guardian ships, we didn't build them at a commercial price and sell them to the pacific nations. We gladly and freely gave them to them. As many they wanted. We would help crew and train and maintain them as well. Any NZ order would be minimal, and the increase in volume means no one really cares about cost to build. NZ would have to pay market price for non NZ equipment, and tomahawks, mk41, essm II, aegis, Sm-6, NSM.
But the biggest and ongoing issue is that Australia and NZ want fundamentally different things. Australia has a history of project requirements going sky high, and costs blowing out in money time and capabilities as we go big. Our military procurement process isn't exactly flawless either.
Throwing in another partner, who would want equal peer input into the ship design, needs spec, local content, but only order<10% is why many euro ship projects fail.
One of the more fundamental issues would be crewing. Another could be ice capability or sea keeping. Another could be offensive weapons. NZ doesn't even operate ESSM anymore.
I think once NZ failed to order ships three and four and then failed to match Australia's upgrades then the whole Anzac joint procurement experiment failed.
I think the ANZAC project was fairly successful. Australia and NZ didn't go to war after the project completed. As an Australian it is very satisfying to watch the Kiwis get roasted by Canada on their Anzac upgrades.
However, Australia has also had fails too. We had to rely on the Kiwi's for Canterberry.
Nice if we can procure together or alongside. But we certainly don't have to force it together. Particularly with things like Ships. We don't have to operate the same surface combatant. Just like Australia and the US don't have to operate the same surface combatant.
In many cases, I would like NZ to benchmark Norway or Sweden for its military. Everyone in Australia would be totally happy if NZ was equipped as well as Norway.