I've been re-reading through Dune recently, and I've been considering the prophecy of the coming of Mahdi that the Bene Gesserit supposedly implanted on Arrakis as part of the Missionaria Protectiva.
From the perspective of the Bene Gesserit and Jessica, it's not a real prophecy, but rather a superstitious myth that they intentionally seeded in the people of Arrakis many generations ago so that they could be more easily controlled by members of the Bene Gesserit when necessary. And Jessica recognizes and makes use of these opportunities straight away after arriving on Arrakis, playing into the roles in the myth.
However, multiple characters repeatedly observe that the part of the prophecy that refers to Mahdi keeps lining up uncannily with Paul in ways that I think wouldn't make sense if this were a purely artificial prophecy seeded purely for the purposes of control. Paul doesn't know about the details of seeded prophecy (and in fact I'm not even sure if he knows about the Missionaria Protectiva at the time he arrives on Arrakis, though I don't recall for sure if this is the case) and so he can't intentionally play into it. He just does on his own naturally. And of course, Paul eventually does become the Kwisatz Haderach and essentially fulfills this prophecy, beyond even the expectations of the Bene Gesserit.
So my question is about how this prophecy came about. Some possibilities:
Was this prophecy actually a real prophecy?
Prescience is an important theme in all of the Dune books (or at least the ones written by Herbert, which are the only ones I've read), and while Paul is the first Kwisatz Haderach, there are others instances in the books of people having minor powers of prescience without being a full Kwisatz Haderach, so I'm wondering if this prophecy could have actually been the result of a prescient vision, perhaps even without the Bene Gesserit being aware of it?
Alternatively, was the prophecy specifically about the coming of the Kwisatz Haderach?
Perhaps the Bene Gesserit's plan was for the Kwisatz Haderach to eventually arrive on Arrakis because of the extreme importance of that planet, and therefore seeded a myth there that would support their plans and ensure loyalty to him when he arrived. This seems very much in accordance with the way the Bene Gesserit operate, and they did know things about how the Kwisatz Haderach would present himself, but given how old the legend of Mahdi is, that their plans went awry, and that Paul was never supposed to be the Kwisatz Haderach, and yet things still lined up to an uncanny degree with him, this doesn't seem quite right.
Could it all just be coincidence? That doesn't feel like a satisfying answer to me. There are few coincidences when it comes to either of the Kwisatz Haderachs that emerge in the books. But then again we are talking about a time long before the coming of the first Kwisatz Haderach.
Or perhaps there's another explanation?