Heroes should be allowed to kill but not as a standard. The hero's priority is to bring the evildoer to face justice. Failing that, the hero should incapacitate the evildoer from being able to continue visiting evil on the innocent. At this point, if it becomes necessary to kill because every other option is proving futile, then killing it must be.
Besides, you know how difficult it gets to create new villains if your hero is killing them left, right and centre?
The Joker should have been killed off ages ago; if not by the Bat then by the law - although he is insane and therefore cannot be held responsible for his actions, which is how he escapes the chair.
In terms of the law, a person whose act or omission constitutes an offence, and who suffers at the time from a mental illness or defect which makes him incapable of appreciating the wrongfulness of his act or omission; or of acting in accordance with that appreciation, will not be criminally responsible for that act or omission.
The difference between lies between the cognitive and the conative respectively:
The cognitive refers to insight, or appreciation of the wrongfulness of an act.
The conative refers to self-control, or acting in accordance with an appreciation of that wrongfulness.
So it may be argued that as much as the Joker knows he's acting illegally (and this is not always true), he lacks the self-control to not continue down that road as it were. Without a strong case for mens rea, the Joker is able to escape conviction.