In almost 50 years of deer hunting I have shot 1 that was running. It was a close, straight away shot and I got lucky with what could be called a bull's eye. The deer was landing on its front legs and the angle of the shot caused the bullet to immediately enter the spine. It dropped the deer in its tracks, the deer wasn't gut shot and there was no external or internal evidence of a gun shot wound. It was the weirdest experience I've had while field dressing a deer.
That one shot, which was my second deer, convinced me that too much can happen, between the time I decide to pull the trigger and the bullet gets to the deer, for me to be taking a chance shooting at a running deer. I had to admit to myself that the "bulls eye" wasn't what I was aiming at. A couple of inches in nearly any direction could have resulted in a wounded and lost deer. I just don't want to kill a deer bad enough to risk that happening by doing something on purpose that has a high potential of failure.
