I'd argue that it's also a problem of biodiversity (at least in the U.S., don't know about New Zealand). If we hadn't eradicated almost all wolves, coyotes, foxes, birds of prey, weasels, and I don't know what else, nature would have solved the problem already.
Now that is hubris, what the hell do we know about long term net positives? Selfish warm feelings, while watching the reality of introduced extinction take place in a matter of mere decades. Pardon me.
Non-native introductions usually have the issue of such a sudden population explosion that the prey cannot adjust in a timely fashion and get killed very quickly, very suddenly.
I grew up in Virginia so here's one specific example: https://dwr.virginia.gov/wildlife/deer/deer-management-progr...
With deer, the problem is often not an excessive population but rather their tendency to stay in one place, destroying young shoots and plantings and hindering the growth of the plants we care about.
In contrast, with predators they cannot stay in one place for long enough, allowing most plants to outgrow their vulnerable size and survive.
Also removing native species and sending the balance out of whack is different to removing a non native species that has sent the balance out of whack.
This isn’t quite accurate, though. Between removing the fence and getting fence construction inclinations, a lot of time has passed, and in the meantime, nature did lots of stuff we hardly understand.
Assuming otherwise is just repeating the same mistake again. Feral donkeys might be part of a new ecosystem now.
And we can be fairly sure about some things.
Rats in new Zealand, rabbits in Australia, cane toads in Australia, etc, etc.
Further it takes time to remove these populations, so you can observe what happens when they're removed from a local area.
Not by any means do we understand enough about ecosystems to justify the hubris to declare any animal as a net negative effect to the environment.
In western Europe, hunters argue they need to cull deer, for example, to keep the forest in balance. That is only true because a) they make an effort to feed the animals during the winter, helping more to survive than otherwise would, and b) because natural predators have been eradicated in the previous centuries.
Don’t ever trust someone that attempts to justify culling a species for the greater good.