New Zealand aims to eliminate some introduced predators — rats, possums, and stoats — to protect kiwis and other native birds.

We exaggerate the extent to which native peoples actively protected nature. Humans have a tendency to hunt animals to extinction, until they learn better. It was the Maori that wiped out the moas, and presumably the aboriginals of Australia that wiped out the giant bird Dromornis, and presumably the Malagasy that wiped out the elephant birds.

Fortunately, humans can also learn to protect nature. In the 1700s, European traders organized a system of territories to limit hunting of beavers in Canada, so that the natives wouldn't hunt them to extinction and bring the profitable beaver fur trade to a halt. This was good for all the humans involved, as well as for the beavers as a species.

The question is whether today's civilization can learn to protect nature and work hard enough to succeed in doing it.

2050 might be fine as a target for eliminating those predators from New Zealand, if civilization continues so that New Zealand remains able to carry out the plan. But that slow time scale offers plenty of time for something to happen that would bring the effort to a halt.

Meanwhile, what about the cats? Domestic and feral cats kill tremendous numbers of birds, all around the world, including endangered birds.

The world is full of eco-menaces that humans actively keep in check. These include invasive species, pollution in the ground, and nuclear waste. If technological civilization falls, there will still be humans (I expect), but they won't have the means to stop these menaces from spreading.