In close to 40 years of elk hunting I’ve only seen 3 elk knocked down without a central nervous system hit and it was with the 338. Of course as a precious poster put it you don’t get to hunt a lot in Az. We have packed into the Gila wilderness several times.
The quickest elk kill that I have made was my second largest 6x6 bull that simply collapsed when I put a 115 grain Sierra GameKing bullet from my .257 Ackley just behind his shoulder.
I've had a number of other bulls and one cow that didn't take more than 3 or 4 steps after I put a 180 grain Nosler Partition from my .30 Gibbs, or a 168 grain TSX or TTSX from my .300 Weatherby, or a 160 grain Accubond from my 7 mm RM right behind their shoulders.