The two primary races of Middle Earth, those created by Iluvatar, are Elves and Men. And until quite late in the history of Middle Earth, the Elves were BY FAR the more significant of the two. They alone seemed capable of Magic, they performed most (by a wide margin) of the great deeds of the first few Ages, and even those Men of great renown, like Aragorn, are heavily implied to be so great because they are part Elven.
The accepted answer to this (Why does Saruman identify himself as a human?) question indicates that they WERE "human", in the sense of "given human form." But as a writer, it seems more natural for Tolkien to have made them Elven, since Elves were more prone to supernatural wisdom and subtle magic by nature.
So why did Tolkien choose to have the five Wizards appear to be Men? Was there any significance to making them non-Elven, or even unique and not like any particular race? Was there an earlier draft where they WERE Men (not just in shape but in lineage), or shared some special relationship with them? Was the exact nature of the Istari even decided by the time The Hobbit was published? Or was Tolkien just pulling on archetypes like Merlin and Prospero, and that naturally led to human-esque Wizards without any deeper significance?