Plainsman -
Here in Colorado I have hunted elk for 20+ years. During that time I have seen more elk wounded with a .243 Win than any other cartridge. Whether the poor results were due to poor shooting , a poor choice of bullets, bullets that were well constructed but simply too light for elk-sized game, or whatever, I can only guess. During that same time period I have seen elk that were taken with a well-placed .243 Win without a problem.
The .257 bullets include some very good designs - in the 120g weight you have Speer Grand Slams, Nosler Partitions and Swift A-Frames. Just a step downat 115g you have the new Barnes TSX. Are these excellent bullets heavy enough for elk? Maybe. Depends on where you put them.
On other forums I have read posts by people who claim to have reliably killed elk with a .257 bullet, and I have no reason to doubt them. At the same time they hinted strongly that there are better choices, which I also believe.
As a long time 7mm Rem Mag hunter, I can attest to the reliability of a 160g Grand Slam. Success with the 7mm Rem Mag has led me to believe that a 150-160g bullet with a Sectional Density of .260 or better is a good minimum. The .257 falls considerably short in the weight department even with the heaviest bullets.
It has crossed my mind on more than one occasion to try my new .257 Roberts on elk this fall, but I keep coming back to "if it ain't broke, don't fix it" -- my 7mm Rem Mag and .45-70 will probably go instead. If you have a .270 or 7mm or bigger, they would be a better choice in my opinion. If you don't, its an excellent reason to get a .300 or .338 Win Mag.