Never had a problem with bleeding out after decapitation, but then again we don't use blunt tools, lol. A blunt implement would indeed crush rather than slice cleanly but if the animal is decapitated it will bleed out anyway.
Note about the knife to the brain method, some people have had some pretty gory issues with that one, even when the brain matter is definitely damaged as per the ideal execution of the job. One description I read on that method had the bird raising its head and looking up at the person that did the 'pithing' while brain matter and blood poured out of its mouth. Wow, is all I've got to say on that one. At least it wasn't doing that unsightly flapping? No consolation to me, lol.
Our mishaps with the axe still killed the birds, much less room for error, whereas a knife to the brain is debatable. Done right, it should of course be humane, but how does one determine for sure? One doesn't, it seems, one just assumes it's humane because they can't show you whether it is or isn't. Lack of knowing for sure is offputting to me. Brain damage on that scale generally does paralyze, but being paralyzed isn't mutually exclusive with retaining sensation and consciousness, though it can prevent the animal or human from showing that it can both feel pain and is conscious. That's the stuff of horror stories, IMO.
If they're paralyzed by it they won't flap, but lack of flapping doesn't guarantee it's humane. If I've screwed up a cull I want to know, not think it's humane because the animal can't express its agony.
Bottom line is, most methods can be humane when done right, but there's room for error no matter what they are, so we all do our own research on it and arrive at our own conclusions on what's more humane. That, and experiment. Animals do tend to suffer while we learn to cull no matter what method we choose.
Best wishes.