But don't you think it's important to recognise that a frigate has utility outside of armed conflict, which seems to be the only duty you mention (escort landing forces, resisting an attack on the homeland)?
Sure, a third frigate might be of debatable merit in an invasion scenario, but how likely is that? Look at how the current frigates have been used (operations in the Gulf, in addition to more regional duties in the Solomons, East Timor etc), and in that context how would a third not provide a significant gain in capability?
I understand your point re supporting an army that lacks other fire support options, and admittedly I don't know a great deal about how naval responsibilities work, but it seems to me that you're arguing from a strange position if you think a third frigate is limited in its duties to fighting off invaders and escorting landing forces.
I'd also argue that a third frigate is significantly more politically tenable than rocket artillery and attack helicopters, given the nature of NZ politics.