Everything you said is true. And 100% irrelevant to the main point I was making which seems to have gone undetected. So I'll repeat it:
But the main difference is, if you're bird hunting with an unloaded shotgun and a bird flushes, you're not getting a shot. So if you bird hunt with an empty chamber you may as well stay home.
Not true with big game and a rifle.
Trying to chamber a round when you're 30 -50 feet from a deer ain't the best thing to insure success either. Einstein.
I said "big game with a rifle." Not "still hunting in thick timber with a rifle."
Oppenheimer.
I once hunted big game wih a rifle where I didn't chamber a round for the first 8 days of the hunt, and I was never in danger of missing a shot opportunity. Sheep hunting in AK, above timberline. we saw sheep every day, just didn't get within range until day 9.
Not everyone still hunts in thick timber.