If you knew there was a spell that would cause you to self-destruct, what would you do with the only copy of it? If you're the Golem, you'd wear it around your neck, which is pretty much like putting a giant red do not press button on your person. But the Golem has a fascination with self-destruction. Being a Golem, there isn't much under her control, but destroying herself is. She wants to make sure the spell is nearby so she can use it if anyone orders her to hurt another person.
The opposite side of that spectrum is the Jinni's iron cuff. He has no choice but to wear this, a reminder of his slavery. Unlike the Golem, he's used to freedom, and all the iron cuff does is confine him. The Golem seems to get over her self-destructive tendencies in the end—it helps that she has Anna to help her cope with her guilt about Michael and Saleh's deaths. But the Jinni will always remain trapped, and the iron cuff is a reminder of this that can't be removed. Maybe they can bedazzle some little jewels on it to jazz things up.