Two friends of mine in fact do use .243's for elk. That one makes me a bit nervous too though as they have both had bullets go to pieces with barely enough penetration to vitals, particularly on frontal shots. I've killed elk/wapiti with 6.5x55, 7x57, 9.3x57 and .375 H&H Magnum. I can tell absolutely no difference in the effect on the animal between any of these cartridges.

Hit right with a well designed bullet I do not believe elk or any animal of that class are particularly hard to put down. Hit poorly they are all hard to put down regardless of bullet.

8x60 about duplicates the .30-06. Good cartridge.

Incidentally, I have a copy of a study conducted in central Sweden surveying the shooting of about 6,000 älg/moose with a large number of calibers over 7 years {1990-1997}. My experience with elk/wapiti is ditto'd in that survey. Average number of shots to kill each moose was virtually the same regardless of caliber. IIRC 6.5x55 was the smallest caliber included in the survey, probably due to legal minimums in Sweden.