I think you'll find that most, make that all, cartridges will kill with a well placed shot farther than most of us have the ability to shoot well. There are those that champion the 7mm mag out to 600yds, a very long ways. On a thin skinned animal what would make you believe that a 7mm-08 with a proper bullet would be any less deadly? A 22LR is reported to be deadly to 1 1/4 mi! That is a long ways and an absurd comparison but if a 40gr 22 bullet is dangerious that far at it's low muzzle velocity, why would a 160gr bullet at 7mm-08 not be?
The thing I find is that people tend to believe that magnum and 3000+fps cartridges work better a long way off because they 1) are easier to hit with and 2) have more retained energy. I think both thoughts are wrong. First they make hitting no easier. Hitting is a product of marksmanship, not trajectory. When you start shooting at ranges beyond MPB range, you need to become a much better shooter, not find a more powerfull cartridge. And many many rounds will penetrate more than well enough to reach vitals and kill an animal well beyond our ability to hit. Has anyone ever seen a bullet that stuck half in and half out of an animal or even bounce off? Again don't think so.