Nobody is talking about introducing random species, but a ressurected extinct species that was a part of the current ecosystem of New Zealand.
This wouldn't just be reintroducing an animal for fun, but an effort to restore an incomplete ecosystem that was made incomplete by humans. Haast's eagle, the moa, the adzebill and the laughing owl were all made extinct by humans and if humans had never colonized New Zealand, they would still be around.Why do you think invasive species are so bad? because it becomes an escalating situation. You need to keep bring in difference species to control the once before which then kills of current local species.
In regards to the local species, the eagles themselves are a local species.