I can't really say for sure about deer, but I can show 3 examples which help prove the validity of waiting. In my younger days, i did extensive bear hunting (bears were considered a pest and we got a $5 bounty for the ears).Also, i used to guide for spring bear. When you shoot a bear, if you wait, they will crawl into the densest cover they can find, and hide, waiting to die. if you chase them, they will run until they drop. i have seen this dozens of times. Ruffed grouse are another example - if wounded, they will try to hide as deep as they can, and lie there to die. if you chase them, they will go as far as they can. the final example - I had 2 dogs that died when i was younger. In both cases, the dogs hid away from us, in a quiet place, and waited to die. i don't know what would have happened if we had disturbed them (just so you don't think I let my dogs die, one had been hit by a car, and we found her dead that evening, under our porch, the other is a bitch that had just had pups. She brought the pups to my mother, one at a time, then asked to go outside. We found her dead behind the garage).
Anyhow, I'm a firm believer in waiting. However, if it turns out I'm wrong, and this can be proven, i will gladly change my methods. Anything to prevent game from suffering needlessly.