Wounding a game animal is why I try to get as close as possible, or pass on the shot which I have done several times. An animal crawling off to die leaves a very bad taste in my mouth....very bad. 350 for Big 6x7 Mule Deer longest. (custom .257 wthby 110 Accubond one shot dead in tracks..Missed Coyote at 8 feet with 22.250 heavy barrel Remington tack driver(he was flying literally), Where I often hunt the longest shots are maybe 125 yards with the occasional 450yd possibility.
While I understand, the deer in question from 38 years ago was not wounded by the cutting of his chest hair and splinters to his body, and the same deer was killed later that season. Also, in my youth and with "target fixation", I never noticed the sizable limb several feet in front of the game, and in fairly obvious Southern swamp undergrowth, I should have.
As for distance and while I have hunted in many locales, I live in the great West where many shots can reach to the horizon. MANY areas and game do not present themselves with short or midrange (SR-MR) opportunities, and in some cases, attempts to close the distance will only result in losing the game to flight or take hours to cross canyons or climb very steep terrains allowing the game to travel some distance out-of-sight.
Game animals can and are wounded far more at shorter ranges than by trained and competent LR shooters who understand their and their equipment's abilities. For many years, I lived back East, and I saw and heard many failed hunting adventures that resulted in missed, wounded and slow deaths to game.
Like most things in life, everyone has different abilities, training, skill sets and confidence. YMMV