I think we would all agree that we should practice and become proficient with the shot we are attempting on any game?
I would venture to say that some of the people replying in this post that are advocating shooting at the animal until it is down have not practiced and become proficient at shooting a running animal. Furthermore, I would imagine that they have not practiced at shooting a running animal while identifying all objects beyond their target.
This adds the element of safety in the woods doesn’t it?
If you shoot an animal (hit it or not) and the animal presents a follow up shot where the animal is again stationary and you can now again identify everything beyond your target by all means go ahead and take it. But I don’t think that is what many of the folks posting here are talking about. IMO they are saying “let the led fly” until it’s down running or not.
That, in my very strong opinion is not safe