Large cats are the polar opposite of "invasive species", moron.
Instead, they are an "endangered" species, worldwide. Why? A lot of reasons, a key one being low reproductive rates. Almost all invasive species have high reproductive rates. Big cats do not. Look up the word "endangered"; you seem to confuse "invasive" with "endangered".
Countless countries around the globe strive to protect large cats as a result. They routinely transplant them to safer and different environments to keep them from going extinct.
I'm not saying that Hawaii should allow large cats; that's up to the state. But Hawaii seems like a perfect environment to allow big cats to thrive, reproduce and replenish the species. The downside? They eat some goats and sheep and make ranchers mad. The upside? They feast on rodents intrusive to Hawaii, and perhaps replenish the species while providing some entertainment for the locals and tourists.