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I think the staffs were given to the istari as a way for them to channel some of their inner power. Remember they weren't allowed to use their full power output against Sauron. The staffs were probably created to let them use some of that power. Without them they'd be trapped in mortal flesh with their power sealed away much like the eagles. So by breaking Saruman's staff Gandalf broke the little access Saruman had to his maia power.
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