All big game animals in the United States are managed, and have been for more than 100 years. If they hadn't been, many of them would be extinct, like the passenger pigeon. When tags are issued, it is for the purpose of maintaining the herd at an optimal level. If too many or too few animals are taken, then adjustments have to be made the following year. Elk herds are fed during the winter to boost the number available to hunt in the summer. There are more similarities between herds of "wild" animals on public lands and herds of cattle on farms than we would like to admit.
Taking that into account, there have to be differences between public and private motivations for hunting. From a public policy standpoint, the hunter who arrives on a helicopter and shoots a trophy 500 yards away is providing more of a public benefit than a hunter who hikes in with his homemade bow and arrows to hunt for some meat. The helicopter hunter spends more money, both in equipment, guides, and fees, and is more likely to fill his tag and less likely to wound an animal. He probably has less impact on the environment than a hunter who walks in from the trailhead and sets up a camp for two weeks, and certainly less than hunters who get to their hunting grounds on ATV's. Any benefit to society of having hunters who are trained in the skills of getting close enough to game animals to shoot them with a traditional bow would be a hard argument to make, apart from the stalking skills already taught in certain units of the armed forces.
So that brings us to private motivation. At a very basic level, is there any difference between the motivation of someone who rides in on a helicopter and shoots a trophy at long range, and someone who walks in with his homemade bow and arrows to hunt for some meat, assuming both have the money and could buy meat cheaper at the store, considering all the costs of hunting, including alternative uses of the time spent? Frankly, I have no idea what the motivation of a helicopter hunter is, but it must be pretty strong, since alternatives would include things like sitting on a beach watching topless babes in the south of France.
Closer to home, most of us have a better idea of the motivations of a traditional bowhunter. But are there different motivations for one who hunts with a rangefinder, and one who hunts without? How about binoculars? I don't think there is any bright line that separates a "true" bowhunter from someone who is taking unfair advantage of the game. There is just a continuum between someone with a compound bow and all the gadgets to someone hunting with only a homemade bow and arrows and a hunting knife.
I think in the end, we each have to establish our own goals and be true to ourselves.