I guided elk hunters for awhile, a little over 20 years. I wouldn't go out and buy a .243 for an elk rifle, but I sure would have a lot more confidence in a guy that could shoot a .243 well, than I would in a guy shooting a magnum that he was afraid of. When working as a licensed outfitter my advice to my hunters was that if they weren't already shooting a mag, don't go out and buy one just to hunt elk. Most guys did better with the deer rifles they were acustomed to. IMO a magnum is best used by those looking to increase their range beyond the 300 yds that the '06 based rounds are adequate for. I wouldn't hesitate using my .243 on elk, assuming relatively short ranges, say 150 yds or so, heavy Barnes or partition bullets, and broadside shots. I think of it as a varmint round that, with proper bullets and positive shot placement, can be used for elk.
CoBrad, This has been my experience too.
I watched a 14 year old shoot a broadside cow at 150 yards with a .243. The cow was hit hard right behind the shoulder and still standing. I told the boy to "shoot her again" and his dad said "naw, hit good". The cow proceeded to put itself together and take off with its calf. A few miles of deep snow and mountains later I got the kid another shot and he put one in the neck. While gutting her out I found one lung destroyed and no exit wound. Using a factory 100 grain load. With something that penetrates better it is likely both lungs would have been taken out. Premium bullet or bigger gun.
I grew up with a guy who only used a .243. Neck and head shots inside 100 yards and he never missed or needed another shot. Not what I would advise others to do either.
I do not think you need a massive magnum, just good shot placement with a good bullet. I know one hunter who has killed a dozen elk or more with a 25-06 - including a nice 8x7.
To get a youngster started, I like what a buddy did. He has two Rifles of the same make and model. One in .243 and one in .308 (has muzzlebrake). He let his kid practice at the range and in the prarie dog fields with the .243 using smaller bullet. When elk hunting time rolled around he put the .308 in his hands and said the brake made it shoot like a .243. When a shot was presented, the boy shot and the elk went down. Like any other first time hunter he never even noticed the recoil or the noise.