You are right about Africa providing more opportunity. Of course, some of this is exaggerated today by "game ranch" (fenced) hunting in South Africa and some other countries, though even that isn't necessarily shooting fish in a barrel. There are some tiny properties where animals are essentially put-and-take, like hatchery fish. But a fenced ranch of tens of thousands of acres is something else.
But most of Africa is fre-range, and even there the numbers of animals are far higher than in North America, for two reasons. First, winters aren't severe, though droughts can be. Second, there are far more kinds of animals. Even if you split North American big game animals into record-keeping categories, there are only about three dozen. In Africa there are at least 80 kinds of horned game alone.
All of this results in an abundance most Americans can't even imagine. Your point about 8-10 big mule deer or elk is actually fairly accurate. I have seen at least 50 MATURE kudu bulls, the equivalent of a 300" bull elk, in unfenced country in Namibia in a 10-day hunt, and over 1000 impala in one day in Tanzania, including a pile of mature rams, and single herds of over 1000 Cape buffalo in Botswana.
This is partly why African trophy standards for a week or 10-day hunt are higher than a North American hunt for mule deer or elk. Over there you're not just looking for a "legal" animal to kill, like a brow-tined bull elk in Montana, but a truly mature bull. The PH simply won't let you shoot anything smaller, and there are enough kudu in many parts of southern Africa that the only reason for not bringing home a good trophy is the search looking for an exceptional trophy. So there's no real reason to shoot beyond 350 yards--or 350 meters, however, you want to measure it.
Also, there's the standard African policy of charging a trophy fee anytime blood is drawn, whether or not the animal's recovered. This cuts down considerably on chancy shooting, whether at short or long range. While good African trackers (whether black or white) are fantastic, they aren't superhuman, and without some luck aren't going to be able to find an animal that's not pretty hard-hit, especially when the animals live in big herds--and many African animals do.
Plus, the meat is normally either sold or given to local tribes, so there's an additional incentive to recovering game, either monetary or necessary for hunting access. So in addition to the basic ethic of attempting to avoid wounding animals, there are other incentives to pass on iffy shots.
Then there's the terrain. While there is some open country in Africa, even there the thorny ground cover sometimes doesn't allow for the steady shooting positions required for long-range shooting. And even if the shooter can get steady, the animal may not be entirely visible. There are exceptions, since parts of South Africa and, especially, Namibia are a lot like Arizona or Wyoming, but again they're exceptions.
Much of the best hunting country is more or less level, but covered with thornbush and trees. In a lot of bushveld a 200-yard shot would be very long.
In many countries there's also the residual British-based hunting ethic that regards getting as close as possible far more commendable than making a longer shot.
So yeah, there is a considerable cultural divide.
“Montana seems to me to be what a small boy would think Texas is like from hearing Texans.” John Steinbeck
