Also, in the books (which I should admit I’ve not read), what exactly were the BG expecting would happen after creating their Quisatz Hadderach? I can’t conceive of how they would hope to retain control or, perhaps rather, how their usual manipulation strategies wouldn’t have blown up in their faces. Would the person they were looking for be so vulnerable in that way? Would they not still have the capacity to retaliate?
Paul is responsible, this is his goal. He used the tools that the Bene Guesserit instiled into the culture to make him a savior and justified his revenge jihad.
The BG didn’t want this, IIRC, nobodies really know what the plan is when the Quizatz Hadderach will happen. Probably that he will become emperor and prepare everyone for a time of peace, however there’s, in the books, something lurking at the edge of the Galaxy. The BG know this and other factions too