game biologists just like deer or elk. They need to be kept in check population-wise just like any other big game animal in harmony with the North American Model of Wildlife Conservation.
Mountain Lions are not only not threatened, they're population are strong and even expanding in many areas (a good indication is that they're hunted - hunting populations in danger of extirpation is not allowed). They wreak havoc on Mule Deer populations year round, and especially in the winter. Mule Deer incidentally, while not threatened by any means, have been in decline the last 8-10 years and this decline has been a serious concern for game and fish agencies throughout the west.
As far as hunting Mountain Lions, using hounds is the most effective way since they're so reclusive and shy. I know a few guys who kill them using the "spot and stalk" method, but it's EXTREMELY difficult. When hounds are not allowed and Mountain Lions aren't kept in check, you get depredations on domestic stock and even human conflict - think the famous llama killer in CA or the first ever Cougar related fatality in Washington state last year.