OK, I have my answer, and there is a big difference between going through UA vs through ANA to get an award ticket to fly ANZ AUS-NZ RT:

With an ANZ award through UA, one can fly from AUS to and/or from any NZ city, including those that require a cnx to reach (e.g., SYD-CHC-ZQN), the limit being only one stopover or open jaws is permitted. This will cost 20K miles.

With an ANZ award through ANA, one can fly from AUS to and from any NZ city not requiring a cnx for 20K miles. If one wants to fly to and/or from an ANZ city requiring a cnx (international flight between AUS and NZ along with domestic flight within NZ), then the award will cost 30K. Apparently, one or two open jaws (arrive A-B, return C-D) don't matter, it is domestic segments in addition to the international ones that take it from 20K to 30K.

I think this is a very substantial difference (20K vs 30K) for the same itinerary. But ANA has the inventory, UA doesn't, so no choice other than to pass on award tickets and pay for the travel. Travel worth > 2 cpm, not great return on the miles, but will pull down the awards with ANA.