Just a theory, and a simple one mind you, but here's mine (I'll post a line below, cause I don't know how to do the spoiler thing)
We know that Salem's forces can't find the Vale artifact, and that led to people assuming that ozpin's came was the item in question. Now I take this video as confirmation of the fact, because, as Qrow said, the only things that the king brought to battle were his sword, and his staff. Staff = cane perhaps? Plus, the fact that the Vale king put the academies right where they needed to be, proves that he had knowledge of the relics, which would further justify Him resorting to one to win the war (like a nuke). This would also give context as to Ozpin's contemplating taking the cane during the fall of Beacon.
Oh, and my theory on Ozpin's reincarnation stands. He doesn't keep doing it. Either he A) just did this as a last resort (like what Qui-Gon and Yoda did at the end of the clone wars cartoon), or B), that the host only has to deal with his predecessor, because if it didn't, the alternative would be far worse, being either C) Oscar's got a ton of personalities raging around his head (which we haven't seen, plus, he doesn't know stuff that predates Ozpin), or D) total spiritual eclipsing/assimilation (which would explain a lack of more voices, but not why he doesn't have memories of before Ozpin's time). C and D don't work, so either way, Ozpin's not immortal, either when Oscar dies, Oscar will co-inhabit some new shmuck, or this was a one time thing that Ozpin pulled to save the world beyond his death.
Or, y'know, this could just be a contrived plot hole.
Thoughts below please.