To rephrase what he's asking without giving an example for all to criticize, for those who consider themselves "Trophy Hunters".....
Would making the hunt for your particular quarry more difficult, give you a bigger sense of accomplishment in the end and if so why don't you do that?
In a general sense such as how you phrased the question, the answer is yes and I do (as most folks on this sight) by using a compound bow during the general season in which all weapons (rifle,muzzle, archery) are allowed. There are other folks that go even further and use a recurve/longbow by choice when they could be carrying a rifle instead.
Your question and his are entirely different and not just two examples of the same thing.