Putting aside questions of ecosystems etc, I think the main reason is that we just can't - ironic since we seem to be extint-ing all the other animals

In South America they tried in the 50s and 60s, and more kept cropping up. They breed so quickly, if you miss an area they can just rebound. Then more can come in on ships and stuff

So you couldn't really localise it, it would have to be a huge global undertaking. And it would likely require widespread use of pesticides that are at best tricksy and at worst illegal, not to mention environmentally shitty