many elephants and buffalo in africa have been taken with a lesser cartrige, and i know either one would kill me if i was shot with em, and as long as the shot is well placed, im sure they would kill an elk as well. it depends on how good you plan on making the shot, and what if you flub up? that 7mm08 has enuf poop to git er done im sure, but do you? i doubt all those buffalo would have fallen to a 7x57 or '06 if the shooter hadnt made a perfect shot.
but then, if you plan on making the perfect shot so you dont need a big gun, why not just carry a light 243win or 25-06? i think that for long distance big game like elk or bears, a magnum of 7mm or larger should be the gun.