Can we just eradicate all foreign comers in the last 200 years from Australia? Perhaps one of the worst losses in Australia has been the near extermination of the native human population by a vigorously violent outside group of humans (who also were the ones that brought along the cats).

Note: this comes from an animal lover (and sure, I have a soft spot for cats) who finds flippant regards like "their complete eradication from the continent".

Nothing should ever be considered for eradication. The lazy solution is to eradicate. The hard solution is to "empathize" (i.e. study the 'problematic' component within a complex system) and figure out how to create a new space for it within the system/reconfigure the system around it.