Page 388 Storey's Guide to Raising Chickens...."Kill the chickens quickly and humanely with a minimum of stress, since stress reduces meat quality.  Of several possible methods for killing chickens, the one most commonly used in backyards is the least suitable.
Using an ax.  Most people's image of killing a chicken is to lay its neck on a stump and chop off its head.  Using an ax is not the best idea, however.  An ax severs the bird's spinal cord, tightening the feathers, and also severs the jugular vein at the same time as the windpipe, letting blood into the lungs and contaminating the meat." 
The book goes further to explain how it can be done by hand or foot or my preferred method after the research that I have done by using a knife.
So I would like to apologize for using the term "contaminate".  Your right blood is edible, and in my opinion sometimes tasty and high in iron.  I still make Booda from my Great grandmothers recipe which requires pig blood as the main ingredient.  However most people I assume, when raising meat birds, do so for quality.  Page 389 Storey's Guide to Raising Chickens...."Bleeding is an important part of the killing process to ensure no trace of blood remains in the meat for the best flavor, appearance, and keeping quality.  It must be done while blood still flows freely."
 
Side note...as an avid deer hunter...if I could get that deer to let me tie it up by the back legs and bleed it out..I would...until then the arrow is going to have to do the trick. Either way I'm still eating it!!!