Half that list DID serve a commercial or food purpose. The other half, excluding rats, were quasi commercial considering their bounty. And that would be why they were extirpated.
Beavers, cats, coyote, hogs, rats, wolves, rattle snakes, SSS with extreme prejudice.
Beavers in indiana were nearly worthless until they were trapped out every where else. They destroy ten times their own worth in timber each year even at the levels they are now. They had to put bounties on coyotes to even get people to kill them. Hogs were never native to Indiana but they did run wild in the country side as it was "fence out" during the early domestication.
SSS, if it's not trapped inside a fence, kill them all. They are useless.