The only difference between the 30-06 and the 300 magnums is the velocity,
The 308, 30-06, and 300 MW all shoot the same bullets. The difference in all 3 is how fast they leave the muzzle. Assuming you need 1500 ft lbs of energy to take an elk the best 308 hand loads runs out of speed and energy at about 500 yards. The 30-06 at about 700 and the 300 WM at about 900. With typical factory loads that is reduced quite about 200 yards for 30-06 or 300 WM, not so much with 308, about 50 yards.
300s or bigger destroy more edible meat than a 30-06
Only if shot at very close range. The 300's shoot the same bullets, at 200 yards they are the same speed as a 30-06 is at the muzzle and will destroy no more meat.
The next question, how far can you shoot and hit an elk?
You also have to balance how heavy a rifle you want to lug around at 10,000' for days at a time. You can keep a 308 UNDER 6 lbs ready to hunt although closer to 7 is typical. A 30-06 is about 1 lb heavier, 7 lb rigs are possible, but closer to 8 is normal. The 300 WM's are usually about 2 lbs heavier than a 308. It is possible to build a 300 under 8 lbs, but excessive recoil is the limiting factor. A 7-7.5 lb 300 is wicked.
I'd use any of the 3 on any animal in the lower 48, and at any range I have the skills to shoot. Considering my long range skills a lightweight 7-7.5 lb rig chambered in 30-06 is the best balance for me. But I'd have no issues with a 308 and good hand loads. Especially as I get older and in rougher terrain.
To be honest anything in the 30-06 class is going to give similar results. I could just as soon pick 270, 280, 7mm RM, 7X57, 7-08, even any of the 6.5's and cleanly take elk out to 300-400 yards, out past 500 for most of them.
If someone can shoot well enough at extended ranges to make use of a 300 mags I have no issue with them using one. Or even if they just want one even if they can't take advantage of it. Personal choice, but you should make that choice understanding all the positives and negatives.
The 7mm magnums aren't as popular as they once were and may be the best western cartridge. The recoil is almost the same as 30-06, they shoot similar bullet weights at virtually the same speeds with similar energy numbers at close range. But the better BC's of the 7mm bullets mean flatter trajectory and more energy at longer ranges, At long range they split the difference between 30-06 and 300 WM.