I know this might tick some people off, but...
It seems to me that most anyone that accidentally encounters a bear, wolf, or mountain lion wishes they didn’t have the experience. I know I have no desire to see them - and I’ve been close to and seen bears and cougars in the wild. Had one lion stalking me. No fun at all.
I am in favor of eradication except for in a few designated places (large enough for the animal’s survival) where people that want to find the predators can. Shoot any animals that get out.
Then we wouldn’t have to worry about our kids getting too far down the trail, or out in the backyard, or whatever. No worrying about predators while hunting/hiking around. We don’t let mean dogs roam the streets. Why let worse than them roam anywhere else? That goes for tigers, etc in other countries - why should parents there have to worry just so the westerners can be content knowing there are still tigers around.
Our grandparents almost had these things extinct - most of us agree they were smarter than we (collectively) are now about such things.
Many pioneers and emigrants had learned the hard way how wolves could be used against a populace such was done in Britain and Europe. We have since forgotten the historical perspective.