Interesting, very interesting....
I think that part of the question is really the issue of what "magic" is in Tolkien's world. I should go rooting around to find the exact quotes, but since the room with all my books is a shambles, I'll have to wing it by memory.
Tolkien has said that in his invented world, the "magic" of Elves, wizards, etc. is a product of their inborn nature, not a power outside themselves which they learned to manipulate. If the staffs of the wizards have any actual power, it is because the wizards, being Maiar by nature, have natural power which they either invest in their staffs as Sauron and Celebrimbor invested power in the Rings. Doing this is always a danger to the maker, because the destruction of the item results in a loss of strength to the one who put that power in it.
We really don't know where the wizards' staffs came from. Did they make them themselves, did they get them from the Valar who made them...? The breaking of Saruman's staff seems to have resulted in a loss of power to him, so perhaps he made it himself (or was directed by the Valar to do so) for some purpose in his task as one of the Istari in Middle-earth. That all of the wizards had them would appear to indicate that they were a symbol or tool of their office.
After considering this issue for a long time (years, actually), I tend to view them as first an emblem of office (like the Steward's Rod in Gondor), and something in which a part of each wizard's own natural power as a Maia was placed in trust to their office as stewards of Middle-earth. Deliberately limited in strength by their diminished life in real flesh, the staffs may have allowed them, in times of great need, to use a greater portion of their natural but reduced abilities, their "magic."
Just my two cents, of course.