How are the native animals gonna thrive when we have cats, rabbits, and cane toads?

The only thing that cares about whether the Bliby goes extinct or not is us. The planet couldn't give two shits about whether somethings a "native" species or a foreign invader.

The surviving organisms left behind after this event are going to expand, diversify and evolve, just like all the other times.

edit: I think I had a stroke while writing the last paragrapb