I agree that no matter what you use, you have to take good, ethical shots.
However, elk have a serious layer of fat that can seal up and stop bleeding enough to prolong the death process. My dad once called me to help him recover an elk that had been shout the previous night. He had bumped into some other guys at the mouth of a canyon the last night of a special hunt, between the lot of them, they had shot two elk, one was down. Most of us went to bone out the one that was down, two guys went to look for the other. They saw it on the opposite hill, still walking. The hunt was over, they couldn't take another shot to put it down. I asked the guy what he hit it with; he said a .308.
Now, I have absolutely no idea how well he had hit it or what kind of bullet he was using. I would hunt elk with a 30-06 or .270, but I think if I did it regularly, I would get a .300 win mag or 7 rem mag. I think you owe it to the animal to put it down decisively, even if the advantage is not that big.