I'm surprised Birdlife bothered picking that up. It is based on an idiotic "opinion piece" article in the Dominion Post which was reposted onto the Stuff website with a clickbait title - here: Kaka conflict: conservation icon to pest | Stuff.co.nz
It is possible for large parrots to become numerous enough to be considered pests. In Australia, sulphur-crested cockatoos don't garner much favour when they "steal" from orchards and cause property damage.
There's no way the same thing will happen with kaka, though.