Mostly a .30 caliber rifle will work fine for North American big game, so let's look at the advantage that a .300 Magnum might have against a .30-06. For the sake of comparison I'll refer to the Hornady flat base spire point 180 gr. bullet.
We will assume both rifles are sighted for 200 yards. The .30-06 has a muzzle velocity of 2800 fps, and our generic .300 magnum has a mv of 3200 fps.
At 200 yards both hit point of aim.
At 300 yards the '06 has a drop of 8" while the .300 has a drop of 6". Chances are a hunter would use the same aiming point with either rifle.
At 400 yards the '06 drops nearly 2', while the .300 drops only a foot and a half.
At 500 yards the '06 is down 4' and the .300 drops 3'.
Beyond 300 yards range estimation, wind, mirage, and ego start to be a problem for the average hunter. For the sophisticated and experienced long range rifleman who has a laser rangefinder and a scope that can be quickly adjusted for long range come-ups and who sets out with the intention of making a long range shot, it is less so.
So at 500 yards our expert rifleman with an '06 must adjust his scope for 10 minutes of elevation, but if he had a .300 magnum he would need to adjust 7 minutes. Does it really matter which cartridge the rifle is chambered for? If we change bullets to the 180 gr. Nosler Ballistic tip, when fired from the .30-06 with a muzzle velocity of 2800 fps this bullet is still supersonic at 1200 yards. We can certainly assume that our .300 magnum might stay supersonic much further, but how far can one expect to shoot with a reasonable expectation of hitting within the kill zone of a big game animal, which we generally accept to be 8"-10"? IMHO this comparison demonstrates that a .300 magnum has little advantage over the .30-06
But what about magnums for power. The .375 H&H is a fine cartridge for hunting big game anywhere in the world, as is the .416 Rigby. As we get into larger and more powerful cartridges, the cartridges become more specialized as we move from hunting rifles to stopping rifles. Once you get into the .577 and 600 Nitro class of cartridges you have reached a power level unnecessary for all but the PH who is responsible for the safety of his client. The client by the way had better hope that the PH armed with one of these guns has invested the time and money to become proficient with it.