Tank,
I think you will find that AKL has a limited amount of alternates for wide-body, CHC being the only one.
Suspect all the larger operators asked for cat III so they didn't miss out on payload, eg. when SYD was the alternate designated.
halas
Ohakea is also an approved widebody alternate. Limited ground support, but it is used regulary, as its only 30mins or so flight time south of AKL.
A year or two ago it had 3 B747s, 1 A340-600, and a B777-200 all divert there at the same time due to fog in AKL (before AKL went CAT III)