The murderer deserves it and his forever absence would be great for citizens...but, it won’t happen because of his previous diagnosis as a schizophrenic.
If he’s a danger to himself then enable his complete self-destruction.
OK, then get a shipping container, insulate it, add three 3” x 12” windows, get a chair, a bed, a desk and a single light bulb. Shove him in and weld the door shut.
He’ll learn what insanity is really all about.