It's just fine as others have said. IMO, the larger calibers only get you distance as they have higher starting velocities so generally have higher velocities at longer range. Higher velocities just ensure big game bullets expand as designed. Expanding meaning more internal damage done in the elk. I know with my 308 I'm limited to about 300yards (according to my ballistic program) with Barnes TSX bullets which need about 2200 fps to expand fully. I can shoot the exact same bullet out of a 300WM and get 600+ yards with reliable expansion. Just check what your bullet's ideal expansion velocity range is, and keep your shots in that zone and as others have said, the elk will be dead. I'd also opt for the heaviest round you can accurately shoot as well. Generally higher mass bullets have better penetration due to higher momentum. Elk are thick beasts, and I personally prefer the bullet to penetrate fully and exit on the far side. Lot's of generalities here, but with a good bullet your 7mm-08 will be more than fine; external and terminal ballistics have a lot of variables beyond that of a single paragraph.
