Way back before the internet, I killed 7 bulls with a 7x57 and 140g Sierra's, and two with a 7 mag with the then brand new 140g nosler ballistic tips. I kept off the shoulders, picked my shots, shots were closer because I was riding a mule(elk never see a man on a mule unless they are running their mouth). All animals died where they were standing, except two that were on a dead run quartering to us. At the impact of the 140g ballistic tips, they hit the ground immediately, tongues stuck way out, front legs quit working, kicked a couple of times is all.
Later on, all we put in for was cow tags. A 243 with 100g partition was my choice, never any problems.
No matter if you use a 458 winchester, if you don't hit them right, you are in for one heck of a tracking job, because they will run down in the deepest thickest canyons you can imagine.
I hunted with an old mule man that had killed or seen killed over 200 elk between Az, NM, and Colorado. He hunted with a 300 Winchester that looked like hit had been through WWI and WWII. He shot Rem core locts, I watched him kill several bulls across a canyons with a darn old 3x9 Redfield, the bulls just flopped.
I think that the biggest mistake a hunter can make is to choose a bullet that does not put a lot of shock on an animal in the temporary wound cavity that is created by the bullet disrupting arteries, and other organs.
I made the mistake of taking my neighbor and his brother elk hunting on my Cadillac mules, and had pack mules with panyards to pack the elk out on. These two did not know how to shoot, gimped up two nice bulls, and we had a heck of a time putting them down after a hellacious tracking job. They just jumped off the mules and started hosing down the elk with their BAR's. I never took them elk hunting again. It is guys like this that make me think of "super bullets" to kill elk with. Also, they don't practice, sight in their guns, clean their guns, and of course want to shoot everything 600 yards and under.
Elk are not hard to kill. The vast majority of elk are killed with a 30/06 with 180g Core locts and a 270 with 150g Core locts.
Before you ever pull the trigger on an elk of any size, ask yourself this question, "how am I going to:
a. get to him?
b. get him out?
Quartering up an elk on a steep mountain side is dangerous to man and beast. If you have to leave part of the quartered up animal over night, then have a plan. Spread moth balls all around the kill to ward off bears and lions. It is a butt hole puckering event to walk up to your elk kill and see that is covered with branches, grass, and bear crap!