Honest answer. Not trying to make a logical case. Feel free to rake me over the coals. I'm on my fourth or fifth moscow mule and the wife has beat me 4 games in a row at scrabble and I can take it.
I am a resident, and quite literally 95%+ of my hunts take place in the general districts of western Montana and have for 25 years, so a 160 inch deer is a big one.
On Thanksgiving day you would probably see me shoot that deer within sight of the BMA box if I could do it legally. I'd chalk it up as a stroke of good luck and a gift from the Hunting Gods with only a couple days left to hunt, and yes, the fact that in hundreds of miles of hunting over the last 4 or 5 years I haven't seen a 160" mule deer buck figures into that. In my head when I hear this scenario, I am in eastern MT, because eastern MT is a damn smorgasboard compared to so much of western MT. If I were miles from motorized access I would shoot it too, and would prefer that and would feel more satisfied and pleased, because I would have experienced the type of hunt that I like best and the kind I likely would have been shooting for when signing into that BMA. But I can't deny that I also still feel a blood lust come hunting season when I see a deer that I would be willing to shoot, as amateur as that may sound.
Though I hate talking about the value of a deer in inches, my answer does change the smaller that deer gets, and so in overgeneralized terms there is probably a gray area 20-ish inches in size roughly between 130-150" where I may not be so sure anymore.
And just to be inconsistent between logic and theoretical deed, if a statewide proposal came along to end hunting season for mule deer 4 weeks before Thanksgiving, I would support it wholeheartedly.