Cats are new by hundreds of years, which means they haven't evolved to resist 1080 toxin.
All the mammals of Australia have been around in Australia for thousands of years and have had long enough to evolve resistance to 1080 toxin as it naturally occurs in many native plants.
The reason you don't hear about this being done in other countries is because their ecological systems are very different and it would be disastrous to release 1080 toxin into the ecosystem.
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Or have natural resistance to 1080 due to it occuring in quite a few native plants.
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Better do nothing then, right? Let's rid ourselves of those pesky native animals, no great loss.