This isn't a war zone. This is a city in another country at peace where he just decapitated somebody in public. He'd be arrested and put on trial. No country in the world would do otherwise. The Americans literally have to launch a military incursion into a sovereign territory to forcibly extract him if they want him back now.*You mention that this sort of rage-fueled violence isn't anything new, especially with soldiers, and that's true. But this sort of behavior is always considered against the rules of engagement and crimes of war. It is not okay, whether it's DeCap America John Walker or real American soldiers in the Middle East. Sometimes real soldiers get punished for this sort of behavior, sometimes its swept under the rug. Often depends on how visible the behavior was to Americans back home.
*obviously that won't happen because it's a superhero TV show; so maybe we should all just stop comparing it to reality, because it isn't.