When I was young, not as smart, and a whole lot faster, I did in a couple with a throat cut. You need a really sharp knife for that, handles on their head, and a rope or harness strap to get there head under control so you can pull them on their side and head back helps a lot. Now I just use an extra arrow. I think I have had spine shots about 5 times in 30 years. Unfortunately I have typically broken two arrows when it happens, and I shoot them again. They usually flop over on the first and often from a tree the second sticks in the ground and breaks when they jump after the hit.
I think many times the animal doesn’t know what happened, and a second shot could be much the same. It would be much more stressful on the animal to be attacked by its killer. I know I would rather get a second shot without knowing it was on the way than have someone jump me and knife me to death.