There are many different perceptions of what "elk hunting" is. I would not count on seeing the portrait of the big bull out in the open in a mountain meadow...after season opens.
Some forms of elk hunting start as close as bow/muzzle loader range.
For at least 100 yrs the 30-06 class of cartridges,and I'd include any full size battle rifle cartridge from .303 to 30-40,etc...and most derivatives, such as 270,etc to be just fine for taking elk. (proper bullet and shot placement,of course)
With respect for First Nation People,"Its not the arrow,its the Indian" is the old saying. The Hunter just does not care so much.You can hand the Hunter a Savage 99 in 300 Savage and He/She will grin and bring you elk tenderloin.
The Classic Superb, elk rifle for at least a half century was a milsurp sporter,or Win 54 or M-70,or Rem 721 or Rem 700,Savage 110, FN sporter,Sako,...Need I go on? Generally topped with a solid Weaver,Lyman,Redfield,etc 4X fixed scope. My wild,unsubstantiated guess would say that describes about 80 % of the elk rifles from the 1950's through the 70's . As variables became more trusted,the trend moved toward the 2-7 and 3-9 scopes,and with more glass came more magnums.
The gun writers I followed still considered 400 yds the far edge of a responsible shot.
None of that was wrong.The elk did not change. A sporterized 1903A3 with a Weaver K-4 is still a fine elk rifle.
I watched a DVD from an "Outfitter" about "Elk Hunting". The plan was crossing ridgelines with the sun to your back,or in the elk's eyes.
The elk were observed across the canyon on the far hillside.Thats when the barrage began. Magnum magazines were emptied and filled.Folks with no clue about long range ballistics or shooting walked them in,hitting legs,hindquarters,guts,jaws,etc till the elk were down,followed by high fives,whooping,hollering,bragging,and celebration.
300 magnum to 338 magnums were typical.Actual ranges were not specified,beyond those estimated during the bragging. It was "cross canyon"
400 yds? 700 yds? Who knows.
Sounds ugly,but that's what some folks do. I've been invited to join in such a hunt. I declined. I won't help with the rifle for that style.
There are a few "long range" elk hunters who essentially use sniper tools and techniques. They might well have the skills and tools to make clean kills.
I don't judge them. To each his own. They don't need to ask "What is a good elk rifle?" They have a pretty good idea already.
IMO? an easy to carry ,fairly light 308/30-06/270 etc rifle with up to about a 40 mm objective,peak magnification from 4 X to 9X,will IMO meet all the needs of someone who actually HUNTS elk.
I've had some interesting conversations with a friend who was a working cowboy and also a Colorado wilderness area elk guide for a major outfitter for a few years.He had some observations on indicators what the hunt was going to be like. One was the client's rifle.
The classic picture of what he rolled his eyes over is the shiny new 340 Weatherby,4-16 "bargain" scope,installed at Sportsmans Warehouse by a clerk,boresighted,with the pricetags still in place.
If you had a moderate ,practical 308,270,etc,it gave him a good feeling.Especially if it looked like you owned it longer than a month. Your boots would talk,too.