Once you have enough power, having more is just a personal preference. It may not help, but it doesn't hurt either, as long as you can shoot it well.
I have used my 375H&H a lot for hunting elk, not because that amount of power is needed, but because I like the rifle a lot, and because where I hunt there are LOTS of grizzlies, and I just feel better with the 375H&H in my hands when I am seeing grizzlies around.
But when I am hunting elk in the places where there are no big bears I have often used my 270s. This year I may take my 8MM Mauser, and/or my 300 H&H. Last year I am my wife used a 270 short mag and a 308 Mossberg MVP. We took our elk just fine.
I do not recommend using minimalist calibers to new elk hunters because many of them come from states where they don't get to hunt elk often, or at all, and you may not want to turn down a shot because it's not quite the right angle, knowing you may never get another chance for a very long time, or maybe never again.
I believe a 243, a 257 Roberts, a 6.8SPC or a 6.5 Grendel will kill elk if you don't try to make them do things you shouldn't, but 270s 30-06s and 308s are all very common rifles to find at most guns stores all over the USA, so when I talk to hunters from other places I usually tell them to bring something of at least 6.5 Swede power or better. A lot more power is fine as long as they can shoot it well.
If someone is going to come out to Wyoming (or any other place) for a once in a lifetime hunt, I would probably recommend they bring something that is not so specialized that they may need to turn down 1 out of every 2 elk they see. Any rifle in the 270 to 30-06 range that shoots a good bullet that will expand and hold most of its weight is fine for elk.
Penetration is important, but we don't need elephant killers for elk. It's fine to use an elephant rifle if you have one and you like it, and if you can carry it all day long at high altitudes in steep country, and if you can shoot it well.
I once killed an elk with a slim wood stick with a 190 grain steel blade on the end. It's called an arrow. I used a wood laminate bow to launch it. I worked just fine.
I have also hunted and killed elk with 44 mag handguns, always with open iron sights and not worried that I would not get another chance, because I live close by and I can hunt them several times a week for 2 months every year. If the shot was not a sure thing I didn't fire. When I fired I killed my elk, and so far every one shot with a handgun was a 1 shot kill.
My old friend Bob Ellis killed elk with his 257 Roberts regularly with factory 117 grain ammo, but he was a VERY good marksman and he would turn down shots that were not perfect. I never knew him to fire twice either. Living when the elk live, you can do that, and not worry much about having an empty freezer.
So if you can hit an elk in the right place with a projectile that penetrates well and give you a wound of 1" diameter or larger, you are going to bring home elk meat, but YOU are going to bring home elk meat, not your weapon.
99% of this is about the hunter, not the weapon.
