For cases like this, I always say "Follow the money ...".
If the aircraft overnights in KKE or any other small regional port, Air NZ has to pay for overnight stay for 2 pilots and the cabin crew, their taxi to/from the accomodation, a dinner and a breakfast.
There is an effect on schedule as you have to allow sufficient rest from the evening arrival until the morning departure. Not to mention fatigue issue of going from an afternoon shift to a morning shift.
You then have to factor in the potential disruption cost if one of these crew calls in sick, and how you get a standby pilot/cabin crew upto KKE, and resultant flow on effect.
At the airport, the people on the ground are having to work half a turn for the early morning departure, and a late night arrival, as opposed to working full turns for a normal turnaround.
So unless you have a crew base in the town, you are having to sell a couple of extra seats to fund the overnight.
I predict the new 6am departure is a tool that will lead to the demise of the overnight as loads for 6am will be less than what they were for 7am.
The other thing is that these regional services normally make some money from the local MP as they travel to/from Wellington once a week...