Given the chicken is being raised with the purpose of meat, the quality of meat does matter and one of the keys to getting good quality meat is proper bleeding. Chopping the head off is not the absolute best in that respect. If the circulation to the brain is cut off by quickly severing the main blood vessels in the neck unconciousness should set in very quickly, well before the heart stops. Having no blood flow to the brain and the head physically detached will have very much the same effect with the slight difference that control signals from the deep brain will keep the heart pumping a little longer.
Certainly this is an individual thing and everyone will have their own standards of what is acceptable, but the practice of bleeding out through the neck has been proven effective and practiced for centuries on may different livestock and game animals.
Also IMHO slittling a chickens neck while in a cone is going to be safer and less messy than the axe and chopping block. Memories of having headless chickens flopping about can be improved upon.