I shot a bull elk facing left broadside looking at me at 42 yards. The arrow hit behind his right shoulder, he had wheeled almost 180 in the time it took the arrow to reach him. I haven't shot at an animal staring at me since. It's still not a guarantee; my first archery mule deer buck was feeding at 21 yards, quartering away - he still jumped the string enough to move forward and turn about 90 - arrow hit the back of the ribs and exited the right hindquarter, fortunately hit major blood vessels and he left a sheet of blood to where he died.
As someone noted, an animal injured with a firearm is seen as "hurt" by the general public, whereas one with an arrow in it was undeniably wounded by an archer. For context, I've put down around 600 injured big game animals, over 500 were motor vehicle collisions, a few dozen were injured with a firearm and 2 had arrows sticking out of them. The rest were an odd assortment of entangled in fences, savaged by dogs or wild predators, starving, diseased or actually healthy but with a healed or congenital injury.
We all hate to see this, but hunter or trapper harvest is a relatively humane cause of death. All wild animals live a short life and die a "bad" death; the other options are disease, starvation, predation, or traumatic injury. Almost no wild animal lives out its maximum life expectancy and dies peacefully of old age.