Not aiming this at @wllm1313,or the OP, but rather just putting this out there. I commend the OP for airing out the question, and here is my response. Its worth what you pay for it.
This is no doubt TLDR. But then I left a certain long range hunting forum site because I was repeatedly warned about violating their,"No ethics discussion" rule. That certain "envelope pushing" hunting techniques can't be discussed in an ethical context matters. At least it matters to me.
I was actually thinking the same thing. Perhaps hunting with a perceived "under powered" rifle is better because you are more likely to avoid taking crappy shots, which even with a .338-378 weatherby mag would not be immediately lethal.

Impossible to prove either way.
If we are going to think this way, let me suggest using enough gun, but going to a single shot to add the "Have to get it right" factor. Back in the 70's, Ruger #1 and Browning High Wall shooters always wanted to tell you they were better shots because they had to be. But they were carrying rifles that would handily kill elk.
I also get the augment that we are likely to practice more with a lighter caliber. To which I say that the Caldwell Lead Sled is a cheap investment.
I'm bothered by the idea that we experiment with how little is enough to cleanly kill an elk. They deserve better. Yes, Native Alaskans kill "almost everything" with a .223 Remington, Swedes kill "all" their moose with a 6.5x55, and people do kill elk with a .243 Winchester. All of these being examples used by those who generally want to go around under-gunned. But the ugly truth is that no one brags about the time it all went horribly wrong.
I've killed elk with a higher end 6.5. I've also had them take 6 well placed premium 180 grain bullets from a .30-'06. Some recent research showed me that the .358 Norma Magnum and 9.3 caliber still have a strong following in Scandinavia. They obviously are not ALL using 6.5x55 there (BTW- they primarily use 156 and 160 grains in 6.5 for big bodied game). For me, and I get this is just me here, the idea of doing our best to get a clean kill should out-weigh all questions about caliber and how far we can "morally" shoot. Even how much farther in we can get by shaving weight from our load-out. I love to geek out on ballistics as much as anyone, but to me ethics requires that we do not niggle around the edges.
Regarding ballistics, one of the key things which makes the 6.5 caliber punch above it's weight is its high Sectional Density and BC, that advantage diminishes rapidly when you go to shorter, lighter weight bullets. Retained energy matters. I do not want to be the guy whose rifle is deadly to 350 yards on paper, but whose range finder says that 400 class bull is at 400 yards.
(Rant about outrageous claims regarding the lethality of the 17 Remington removed)
Sometimes we just need to back up and think about the animals and everything that goes into an ethical hunt. The driving factor of ethics is what happens when it turns to crap, not when everything goes perfectly. Elk do not read ballistic calculators, they are tough SOB's with an amazing will to live.
BTW- There are PLENTY of lightweight rifles in calibers all the way up to 300 Weatherby Mag