I have hunted elk with about a dozen calibers from .243Win to .340 Weatherby as well as some larger diameter calibers like 10mm Auto, .41 Mag, .414 SuperMag and .444Marlin. Where you hunt, how you hunt and what you hunt really serves to limit or extend the distances. I like to have 3x body mass in energy or maintain a velocity over 2200 fps with an appropriate bullet and placement. The .338-06 is my favorite for elk and I can go with a .243Win or .260Rem for Deer and Pronghorn (but any of the 6mm and 6.5mms that have a MV of 2700 fps plus would be about equivalent).

For every "its perfect" you will have someone say it is "overkill" or "unethical." IMHO, I would rather have a .308 for elk than a 6mm or 6.5mm. Out to maybe 350 yards on a good presentation and enough practice under your belt, the .308 is fine. For a less optimum presentation, you have to start passing on the shot, or have a better suited caliber. At 50 years old and hunting elk since I was 13, most of mine (about 40) have been shot with .30-06 (to 420 yards most closer) and .338-06 (to 505 yards) and I have seen about 200 shot in addition to that. Most of the failures are poor presentations with calibers in the 6mm to 7mm range, probably more with 7m Rem Mag than anything else. No caliber is a wonder caliber for elk. Too much meat damage on poor shots to pass throughs without expansion, lack of practice are all factors. Deer and Pronghorn, even bear, are much less sturdy than elk and easier to kill. I'll use .223 (not in CO of course) to .30-06 for deer and having shot 60+ have never had one go more than a 100 yards. Not the same with elk.

There is nothing at all wrong with the .308 or .30-06 based calibers (and the .30-06 is plenty accurate regardless of rustycrustys opinion of it) inside 200-500 yards depending on specifics. You just need to decide what you want more than .308 for and then decide on a good load and practice. Both of my teenage boys started with .308 and now use .30-06 for elk, .243s for deer and pronghorn.

I will say that the vast majority of "caliber" accuracy and failure issues are because most hunters don't practice enough to be skilled riflemen and they don't know their ballistics.