Here's a hugely popular cartridge that was and is chambered in rifles that most anyone can afford. Essentially, it's the 264 Winchester Magnum necked up twenty thousands of an inch to accommodate bullets of 0.284 inches in diameter. The cartridge was announced in1962 at the same time as Remington's new Model 700, which in long-action version replaced the Model 721. Rifling twist was set at 9-1/4 inches (some manufacturers now use 9-1/2 inches) so bullets of up to 175 grains could be used. Some gun and/or cartridge writers crab about that, but I personally think it is the only physical advantage the 7mm Remington Magnum has over the 7mm Weatherby Magnum. The Weatherby uses a 10-inch twist, which tends to limit bullet choices to a maximum of about 160 grains. I like heavy bullets, and especially like the fact that the 7mm Remington does handle 175s, citing Swift's A-Frame as the best of the best.
The 7mm Remington Magnum has a great deal more power than the popular 270 Winchester, and even some apparent down-range advantages over the 30-06. Further, countless elk have been taken with it. Even so, I regard it to be at its best with game somewhat smaller than elk. It is amazing for deer, offering extended range along with the solid impact you might expect of a 270 at, say, 300 yards. I would much rather see a 30 caliber rifle used for elk, or even a 338. However, as stated, many elk have been killed with the 7mm Rem Mag. For mid-sized African plains game, it is ideal.
Insofar as accuracy is concerned, I find the cartridge to be a bit fussy. In most rifles, the point of impact changes more than I like to see when working through a spread of bullet weights. Also, there may be a comparatively narrow range of loads that provide superior accuracy. In that department, the 7mm Weatherby Magnum kicks butt. It tends to be more efficient with heavy loads, providing the opportunity to fill the case to a greater use of available volume. Remington's 7mm Short Action Ultra Magnum provides match-quality accuracy, but the cartridge is all but dead on a commercial basis. Some have called it the 280 Ackley Improved-Improved. In other words, it has roughly the same power as the 280 AI, but even more refined round-to-round uniformity.
A great number of commercial and custom rifles are chambered for the 7mm Remington Magnum. Hunters could certainly do worse. Ammunition is widely available, and overall performance is quite good; kind of like getting a solid B for the semester grade. Recoil is about a 5.5, if the 30-06 is a 5.0. On that same scale, the 270 is maybe a 4.3. Nothing scientific here; I just make it up as I go along, and calls it as I sees it. On that same basis, what would I choose for an all-'round rifle? Well, I'd probably pick the 30-06 over the 7mm Remington Magnum for several reasons... Ammo is even more available; the stalk is an important part of the hunting experience (so extremely long shots on game such as elk are of no interest to me); 30-06s aren't usually very load fussy; 30-06 rifles are typically lighter; and it's almost impossible to wear out the barrel of a 30-06 during a lifetime of hunting. How about comparing the 7mm Rem Mag to the 300 Win Mag? It would be the 300 Winchester Magnum for me. It's just so much more powerful and effective on game (despite what the spec sheets may show), that the little bit of additional recoil isn't worth considering.
So, here we have a darn good cartridge that was swept up in a wave of rock-star popularity, and which is used regularly by hunters to shoot game a little too big and tough for its honest-to-goodness physical capabilities. Nothing I say here is going to change that. Fear of recoil (smackaphobia) has become a major factor for many people selecting a rifle. Whatever they decide, they can then picture in their mind that what they chose will do the job; the elk will be standing broadside, and so on. Think twice... The elk may be moving briskly in the opposite direction, 250 yards away on the other side of that ravine, and it may well take a 225-grain bullet from a 338 Winchester Magnum to drive through to the vitals. Don't let smackaphobia spoil your hunt.