Normally I'd jump in to a debate like this because I'm an environmentalist and conservationist, but I don't know enough about the facts in Alaska so I'm posting here. From what I have seen and read the predator-prey cycle is a boom-and-bust thing, so reducing the predator numbers will not increase the prey numbers over the long term. There will be a short term increase, followed by a long term decrease caused by starvation, parasites and disease. (Read Mark Stanley's post)
Hunting for control is a highly emotive issue. People see animals dying for no real purpose. Here in Australia there is a huge outcry against aerial shooting of animals. "The animals have a right to live!" is the emotion behind the rhetoric.
Well, as an environmentalist and conservationist, I whole-heartedly support the extermination of wild horses, water buffalo, goats, pigs, cats, foxes, dogs (not dingoes), rabbits, donkeys, and anything else that is feral. I think the right to not become extinct is more important. I think bilbies, narla, numbats, hairy-nosed wombats, quokka, palmer wallabies, rock wallabies, leadbeater's possums and coroboree frogs have the right to not become extrinct.
And that is a very real possibility with all the animals on that list.