The way to make the problem go away is thru de-listing, something that is actively being sought with the current administration. Something that takes time, research, studies, lobbying, etc.
Shooting them and writing phony confession letters make take care of a wolf or two but will keep them federally listed insuring no legal lethal control, no hunting, no trapping, continued collaring, continued federal dollars for studies and research, etc.
The long term solution to this problem isn't to try and smash it with a hammer, it to delicately remove it with a scalpel.