I think there is a difference between a "trophy hunter" and someone who appreciates a nice set of antlers but doesn't forego shooting other animals while waiting on a mature specimen, or a person who significantly "handicaps" himself on equipment choices vs an "anything goes" hunter. Nothing wrong with either form of pursuit, but different.
While I'm sure that cave men, and through time most hunters, appreciated a mature specimen because it provided more meat, a larger hide, heavier bones and larger antler or horn for tools, and maybe even "bragging rights," I think they shot whatever they could get with the most "modern" tools of their day, and appreciated all of the kills for whatever they provided. When your very life, and those of your family or clan, depended on it, successfully killing anything is what mattered.
Once we no longer needed to hunt some hunters, found additional challenge and more time and enjoyment afield by being selective in what we decide to kill. That means passing on animals that have not yet reached maturity (eg: minimum 4.5 y.o. for whitetails). It may also come in the form of substantial limitations like traditional guns and bows. Many times it means not killing anything even though the opportunity to do so, or it would have with modern equipment, happened many times during the season.
I kind of like the term "selective hunter" because I think that means foregoing the easiest route be that by limiting technology or pursuing only mature specimens or both.
I think that in the span of human existence it is a fairly recent phenomenon.