The reason Elmer Keith and hunters of his day liked bigger rifles like the .375 H&H wasn't because they were a magnum, it's because they fired bigger, heavier bullets that would hold together on marginal shots at larger animals. Elmer loved the 35 Whelen, too, and shot the record grizzly with one firing the 275 gr round nose at about 2300 fps. Premium bullets were unknown in Elmer's time, and big heavy bullets were needed for penetration.
Magnums for velocity and trajectory considerations became popular through Weatherby in the 50's, followed closely by the Winchester .300 and .264 magnums. Comparing trajectories of the .308 Win., the 30-06 and the .300 WM with 165 gr BT bullet and a 3" radius Point Blank Range (PBR):
.308 Win = 277 yds, 30-06 = 295 yds, .300 WM = 314 yds.
The drops at 400 yds below line of sight for the three are:
.308 Win = 19", 30-06 = 15", .300 WM = 12".
The magnum increases range only about 10% over standard calibers, and does it at the expense of increased weight, increased recoil and muzzle blast, and increased $ cost. And for most people, decreased accuracy, which completely negates the benefits of the increased trajectory.
The main problem with magnums is at closer ranges, where unless you have a premium bullet, they tend to "blow up" and under penetrate, wounding game. At .308 and 30-06 velocities, just about any cup and core bullet will perform well on medium game, and the heavier bullets work well on the bigger stuff. A 200-220 grainer from an '06 just hammers elk and moose and is OK for big bears, because the velocity is low enough for the bullet to hold together until it gets in the vitals, and this without the expense of premium bullets and much more powder.
Today's magnums have their place, but only if they can still be shot well, and if the extended range is needed (>350 yds). Unless I hunted where the AVERAGE shot was 300+ yds, I would take the 30-06 or .280 Ackley every time for medium game, and for bigger stuff like moose and big bears, the 338-06 or 35 Whelen. The 180 gr GMX or the 200 gr Partition are real killers in the .300 WM at any range.