As usual, Mr. Dill nailed it. A more reasonable and thoughtful fellow I've never "met".
As a retired wildlife manager; IN, KS, MO, and retired in KY I fielded such queries over nearly a 30-year career. To answer the OP's question, I recall Idaho had a two-week traditional-only season for some time. I don't know if it is still in place or how wide-spread or popular it was.
I do not like to split the ranks. I define the ranks as all hunters. Like others wrote above, I can hunt with my recurves from the 1st Sat. in September through Martin Luther King day in January. I hunt private land because there is so very little public land in my state, or any state I've ever lived. The only other people I see during the bow season are my son, daughter, and son-in-law. What folks are using on the farms adjacent or near me is not my concern.
Finally, I would be very concerned that a traditional only season would highlight the relative unpopularity of our style of hunting and make us more irrelevant to some folks than we already are.
Personally, I would not hunt in a traditional-only season on principle.