Good grief Charley Brown! [

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Sure it "has" killed some elk, but then likewise a .22LR has been used to take down a pachyderm or two. But that makes neither a "trustworthy" candidate. Cleanly taking deersized game with hopped up .22 centerfires and .24s is a FAR cry from using one to take elk. Sure if you have plenty of time, are willing to let many go in the quest for "just the right shot" yeah the .243 will work for elk. But that is a LONG way from being able to call the caliber a good one for wapiti.
A premium bullet fired into the lungs inside of 100-150yds "might" take one down. But it wont do it quickly. Elk can cover a hell of a lotta land in that time frame. How humane is that? Simply putting a hole in their boiler room isn't enough. Stick that same bullet into the top of the neck and it likewise "might" take em cleanly sometimes. But what about the other times when it doesn't?
I don't know about Milek using a 25/06 for elk. If he did it was under my above mentioned conditions, he was a writer with more than an occasional chance at them and I assure you he didn't prowl around on a place like White Mountain Apache in quest for a B&C class bull with nothing more than a quarter bore! Roy Weatherby LOVED his .257 and occasionally took elk with it, but even he knew the limits of the bullets and that round when dealing with animals over a couple of hundred pounds in size. Besides that, a .257 Wby loaded with something like a 117 Xbullet is a FAR cry from your ordinary .243 Winnie.
Good luck none the less,
RA