I have done well at 400 with a 270. But I have seen it done with 25-06s and several 6.5s too. However I also see some of the elk stay up and on their feet longer than I'd like at those ranges. From larger guns too, but at least if you shoot a larger cal and a good bullet, one that holds together well enough to exit 100% of the time, the blood trail is very good so you will seldom loose one. My 270 with 150 and 160 grain Partitions exit them. So will a 308 with the correct bullet as will a 7X57 again with the correct bullet. I have seen one bull shot at about 375 yards with a 338 Win that ran over a mile. The issue was the bullet, which was one of the old Nosler Ballistic Tip Solid Base bullet, which were one of the very worst game bullets ever made. Clearly a 338 is more then enough for killing elk, but that bullet was a glaring failure.
So ethics get involved, but what is ethical is subjective, not objective. Many other hunters may disagree with me, but in my 50+ years of killing elk, and seeing elk killed, I would say that at 400 yards the hot 6.5s with 156 or 160 bullets are the bottom of the list. In the hands of a good marksman, they will do, but that's is where my list would start, and go up from there. Most elk are killed inside 400 yards and so I am not someone who thinks you need a huge rifle to kill elk most times. But as range increases you loose power due to shedding velocity and the marksmanship to hit a target exactly where you want to is a compounding problem as range increases. that is why the issue of ethics is important, and a marksman who can hit a 6" plate 100% of the time at 600 yards doesn't face the same ethical problem as one that can only hit a 15 inch plate 20% of the time. So the issue is #1 the marksman using the rifle, #2 the bullet used and last, in #3 place would be the cartridge used.
The man is the issue about 96% of time. Then the hardware.
