Ive hunted elk for almost 50 years, Ive seen guys successfully drop elk with everything from a 257 Roberts to a 458 win mag.
one guy I hunt with uses a ruger #1 in 270, and my late hunting partner preferred a BLR in 358 win,
both guys have a long list of successful hunts.
what rifle you select is far less important than your skill using it and knowledge of the elk and the area hunted,
a decent rifle,you already probably own, in a caliber like a 30/06, with a quality 180 grain-210 grain bullet,
in a , bolt action, slide action, single shot or BLR is fully adequate in experienced hands
Id say far more hunts fail due to lack of the hunters physical conditioning, lack of proper knowledge of the area hunted,
or lack of persistence than due to the rifle used

the best combo Ive found for general use where you don,t know the ranges likely to be encountered,
is a synthetic stock 340 wby loaded with 250 grain bullets and a decent scope like this
https://www.midwayusa.com/product/3...pe-30mm-tube-5-20x-50mm-side-focus-matte

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I doubt Id have done any , better or worse with a ruger falling block in 338 win or 35 whelen
or a BLR in 30/06