Although I have no interest in hunting "dangerous game", I do believe that controlled feed is a highly desireable feature in a sporting rifle that is used for hunting of any kind.
While I strive for clean one-shot kills, and put in the time at the target range to help insure that I'll be able to deliver them, the game sometimes has it's own ideas. With a controlled-feed action, I hunt with confidence, knowing that if a quick, well-placed second shot is required, my rifle will deliver it -always, and without fail.
I currently shoot a CZ 550 American Classic in .30-'06 caliber. This rifle will put 5 shots into 1.5 MOA groups, which I believe to be sufficiently precise for the game that I shoot over the ranges that I am comfortable shooting it at. I don't think that controlled feed reliablity and sufficient precision need to be mutually excluisve and the CZ 550 adequately proves that point.
Although I would not personally hunt game with a push-feed bolt action, I know that there are legions of hunters here in this country who have used Remington Model 700's and similar weapons for years with spendid resutls at every pull of the trigger, so I would have to say that for some users, controlled-feed is a "non-feature", subject to personal taste.
Shoot what you've got confidence in and shoot well, whether it be controlled-feed or push-feed, and shot it confidently. For me, doing that means shooting a controlled-feed action. Your results, as they say, may vary.
-JP