I can shoot 10 wolves per year, and up to 10 per day in most areas of the state.
I know a guy who trapped 13 wolves this winter on his trapline.
Even with money influencing big game and hunts everywhere, Alaska has chosen to allow non-residents to hunt wolves without tags in some areas. Residents can hunt them pretty much everywhere for most of the year with a general hunting license (which is free).
The reason they can do this is simple. Wolves are smart. You will not kill them all from hunting/trapping. The only way they were eliminated in the west originally was mainly by poison (which Alaska also employs in certain circumstances to help the moose herds).
Game and fish here released a study around 10 years ago stating they estimated 90% of ungulate death was caused by non-human predation, the vast majority of which was caused by wolves. They do not merely eat the sick and slow. A wolf pack is extremely efficient. They will pick easy targets, but can easily catch and take any animal they choose in most circumstances (especially in the winter as they run across the top of the wind-blown snow as the moose and caribou are post-holing up to their chests trying to get away).
I've been lucky to have seen wolves a few times here. Got shots at some on 2 occasions, but unfortunately missed both times. Probably my most disappointing hunting experiences to look back on. I would love to have them as rugs on my wall, also, would love to have saved those countless caribou/moose.