Oh Boy, I’ve been wanting one of those for awhile. Not necessarily for elk myself though I’ve read they do fine with the right bullet and wouldn’t hesitate if you load accordingly. Someday I’ll have to get one of those laser beams…
I've never shot an elk...you can stop reading at this point and not offend me whatsoever fellow 'sliders!
That said, I do own a 257WBY, and I handload for it. It truly is a laser-beam...pushing a 100grn TSX nearly 3600fps. It also is a relatively pleasant cartridge to shoot...compared to my 375H&H from the bench! I've used that 257WBY load to shoot a handful of spring black bears on spot and stalk hillside hunts. I've cleanly taken all of them with it...two of them were six-footers and one was a seven-footer...all one-shot kills. I've also cleanly taken a caribou with that load (one shot). Last thing I'll add is that I am careful to shoot the animal in the heart/lung area...I suspect the high-speed of that bullet could badly damage shoulder meat (hydrostatic shock), but don't know that first-hand.
Black bear and Caribou are not particularly hard to kill...not sure about Elk (repeated intentionally...and I'm stopping at this point!).