There's no evidence that wolf populations would explode if not managed by humans, so controlling them seems premature. There is plenty of evidence though that wolves help manage ruminant populations which do explode out of control without their natural predator, which just so happens to do a better job at it than us (see deer populations in eastern US).
Not solely. Humans have been hunting non-food targets for about as long as they've hunted food targets.
> There's no evidence that wolf populations would explode if not managed by humans
They (and other predaceous species) currently being managed by humans, just by the government and not hunters at large. The bureau of Fish, Wildlife, and Game has long set poison traps for the express purpose of killing wolves, coyotes, and wild dogs.
It also helps keep the various wild herds/packs from exploding in size, reducing the number of wild animals that die from starvation.
(Bias disclaimer: I don't hunt, but I live in a state where I'm a minority)