To be honest, I don't think I buy this. I'm from NZ and we have a number of introduced species (possums, stoats) which have a dramatic impact on the native wildlife.
A lot of bird species in NZ are unique and only found here. They're almost all critically endangered or at risk [1], as they evolved with no natural predators.
I'd rather we try and control these introduced species so we can keep (at least some of) our native birds.
[1]: https://www.doc.govt.nz/nature/conservation-status/threatene...