Hunting for tradition, for self-enlightenment, for sport, for challenge, or, dare-I-say, fair chase is a relatively new thing in the human experience. Those things have become glorious side effects.
Since we were formed we have hunted for food. That is ingrained in our being. Expecting that the glorious side effects of that basic act are the prime reason for why we do what we do is a fallacy.
The modern conservation effort was designed to mitigate one of our other basic acts, that of developing technology. When our technology overwhelms the resources, restrictions are necessary.
Ever since the modern conservation effort began, high powered rifles have been considered a part of the fair chase ensemble of technology allowed. They are part of the modern hunting ethic.
Your choice not to use these accepted tools is simply that, your choice. To describe your choice as somehow more ethical, more fair, more skilled is arrogant and degrades the community of hunters.