I've hunted elk for over 40 years, killed more than 25 with numerous calibers. 6mm Rem, 7RM, .270 Win, 30-06, 300 WSM, .44 Mag, 6.5 CM, 6.5 PRC, 338 WM and probably a few more that I can't remember. The longest shot was 140 yds with a 6.5 CM and the shortest was probably 15 yds with the 338 WM. Average shot distance is probably in the neighborhood of 40-50 yards. I hunt in timber because that is where I find the elk. We have had our elk camp in the same location since 1988 and with 3-4 guys hunting each year, we have killed 57 elk out of that camp. The longest shot anyone has taken was 435 yds and that was with an old Mauser 8x57 with anemic factory ammo and iron sights, one shot through the heart.
I have sat on the hillside looking across the canyon, probably 250-300 yds in a snowstorm and watched the snow through my binoculars. The falling snow changed directions probably 4 times due to the swirling wind in one pass looking across, looked like a drunk navigating the sidewalk at closing time.
Last fall in Wyoming we were on a cow hunt and I didn't have a tag, so I was kind of acting as a pseudo guide for a guy from MN that had hunted elk a couple times before. It snowed/rained all day the first day and visibility kind of sucked, but we did manage to see a real nice buck feeding on the ridge across the draw. We got into elk the next day but the wind was blowing pretty strong and Rick wasn't comfortable taking a 450 yd shot, well lets get closer. This time the elk were no longer around when we got there, pushed by other hunters. Later that morning we were still hunting through the relatively open lodgepole, quiet going, but could only see 75-80 yards for the most part and that was narrow slots through the trees. I was constantly watching for tan patches, we knew elk were there because they were bugling earlier. I spotted a tan spot, put up my binos, and saw elk hair, but it looked wrinkled. Turns out it was a 5 pt bull bedded about 40 yards in front of us. He finally saw us, stood and peed in his bed and took a couple steps. I kneeled down and was able to see the whole animal, Rick knelt beside me and watched the bull through his scope. Finally the bull had enough of us and walked off into the timber. Rick stood up and told me that made his hunt to be able to sneak up on a bedded bull. He didn't get an elk on that trip, but he had a successful hunt.
I had a cow tag in Utah in 2021. Third day of the hunt I had my partner who didn't have a tag work up the ridge from about a mile away. I was into elk right away, but they crossed over onto private back towards my partner. I worked farther up the ridge and then saw an elk above me, she fed out of sight so I crept closer. I was in the middle of a knee high patch of brush with no cover when all of a sudden I was surrounded by elk, pinned down, from about 40 yards away. I had to stand still and watch them out of the corner of my eye, while they either watched me or fed behind cover. After what seemed like 10 minutes one of the cows gave me a clear shot, so I took it. She went behind a tree and stood there for about 5 minutes. The tree was thick enough that when she walked back out the opposite direction, I wasn't comfortable shooting again until I was able to verify that she wasn't piled up behind the tree. I was able to take a few steps up hill and see that was indeed the cow that I shot that walked back out, so hit her again and she piled up. Had to go the top of the ridge to contact my partner, turns out he had been chasing elk all morning and wondering why I wasn't where he thought I should be, he was kind of pissed until I told him I already had my cow. Turns out the first shot was a little far back and she had exhaled because the bullet went through the diaphragm twice, once each side and clipping the liver in between.
Long way to say that elk hunting is addicting and it is very personal, its you against nature. You are in the animal's bedroom/backyard. You have to attain the skills to be able to get into their house undetected.