I've shot about 25 elk myself and have been in on the taking of around 100 others. Elk are tough and I have always went by the theory of shooting again if it is still on it's feet. It seems to me that by turning your attention to another animal and shooting while it is running can easily lead to having 2 wounded elk to deal with.
You can brag about the gun and the shooter being capable but that doesn't negate the fact that the elk being shot deserved better. Bad form in my humble opinion.