C'mon, Bullhound, did you really expect me to answer such a set up question as "will you give a shit when..." ? (That was the point of my "When did you stop beating your wife?" analogy - it's a no win question. Would you give a shit if I stole your car?)
When that becomes the only way to hunt, I'll do it, if I am still alive then. I won't like that being my only option, but I'll do it. So, obviously, I will "give a shit."
1-pointer - do you really think hunting survives because it is sound game management? Think - government hunters. They already shoot Nutria with silenced .22s at night in some areas so the public isn't disturbed by the sight or thought of killing. The same thing happens in some areas for deer - they spotlight them and shoot them with silencers in the head. The people don't want their lawns or bushes munched, but don't want to think about killing the deer - so the government hires contractors to do it for them without disturbing anyone. When the citizens wake up, the bodies have been hauled away and the blood washed away, too.
California is eradicating the hogs on some of the channel islands with government hunters - no sport hunters allowed on some of them. Same thing in city and state parks around the Bay Area.
Don't count on game management as a reason to keep hunting. It's an argument, sure. But one that can be overcome easily.
What's next? Bowhunting, because it takes the animal too long to bleed out? Or it runs for hundreds of yards before dropping? Or as Moosie pointed, shooting poor old Yogi the bear with his head in a barrel eating donuts? How about hound hunting? That's already been banned in several states.
That's how you get somewhere...one step at a time.