Having had to put down 2 sheep from a dog attack, and a goat stuck in a bush I'd already shot, I sure as heck don't like having a razor sharp knife in one hand and trying to hold a head still for a neck cut on a struggling animal with the other. Even the first sheep which was 4/5ths dead from blood loss put up enough fight to make me nervous: add some stress, low light/dark, difficult footing, rain/dew etc. and it's a recipe for more than one thing being cut.
If I ever have to do it in the wild I'll be shooting another arrow into the heart/lungs.