I see no reason to hunt wolves. I can't imagine the meat tastes all that good.
Only humans of our "civilized" culture think that it's okay to exterminate the competitors of our food. Protecting your food stash or life from an immediate threat is one thing. Systematic extermination is an entirely different idea and one that only the "civilized" could think is reasonable or ethical. I don't think the problem is about too many wolves or about too few deer or elk. It's about too many humans. We humans lived in balance with nature for almost 250,000 years. Somehow, in the last few thousand, we've gotten the idea that we're exempt from nature's laws and can do as we darn well please. Oh well. Not much I can do about that. But I certainly won't stand in the way of the wolf's resurgence. Personally, I'd celebrate it. I'd prefer to let them be -- wildlife can fend for themselves just fine without our intervention. If anything, our intervention is their biggest problem.
As for livestock, they can go where evolution intended them to go a long time ago -- extinct. But that's my personal opinion and I'm not a rancher or farmer. Obviously, I'd think differently if I was.
There's a story about wolves and their effects on the Yellowstone ecology. I'm not educated enough to evaluate the study on a scientific level but it seemed to make intuitive sense that a balanced ecosystem benefits all levels of life. I'll happily hunt alongside wolves, coyotes, mountain lions and bears (and risk being hunted by them).