Can we completely excise Arkham Asylum from the Batman mythos? It's really not a great way to treat (or present) the mentally ill.
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The easy fix is to just represent Batman villains as criminals. Flamboyant style, weird tics, but never "insanity defence" ill. Then, prison
If you actually need a creepy insane asylum for your story, maybe set it in an era when they existed and functioned like that
