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?
He is, and he knows it. Throughout the book he references a “terrible purpose” that has been thrust upon him, which is the slaughtering of trillions (and may also refer to the Golden Path, which is mentioned more in Children of Dune and later books).
The in-universe translation for Kwisatz Haderach is “Shortening of the Way.” The BG basically wanted a male Reverend Mother who could bridge the gap between the shared memories of the BG (the past), the present, and the future using the KH’s prescience. Paul wasn’t supposed to be the KH, nor was he supposed to be a male. Jessica was instructed by her BG teachers to produce a girl, but she fell in love with Duke Leto (she wasn’t supposed to), and gave him a boy (BG can control these things).
The theory is they were likely looking to control the universe with this One who could see everything with their prescience. Paul could, and carried out his great jihad to control the empire, but not for the BG. The BG also fucked themselves over by planting the prophecy amongst the Fremen thousands of years before the events of Dune, which heralded the arrival of Paul and his mother, which the Fremen believed and allowed Paul to rise to power.
The KH was always supposed to be male. He would have access to paternal memories the way that Reverend Mothers have access to maternal memories.
As an aside Hebert was operating under a theory in vogue in the 1960s that memory was coded in DNA. Women lack a Y chromosome so they had no access to male memories. The KH would have an X and a Y so he could see everything (ignore that Alia seems to have a copy of Baron Harkonnen, just a plot device that fucks everything up).
Jessica’s daughter was to be bred with Feyd Rautha to produce the KH. So he arrived a generation early, and outside of the careful education/indoctrination program they had planned.
Edited: all my KHs became KWs…because KW is a thing that deserves autocorrect?