The BG go around the galaxy seeding myths to primitive people, no? On Arrakis this was the messiah myth, presumably messiah myths were seeded on other "primitive" cultures as well. When the KH shows up, then he will present himself as the messiah to the primitives, and no matter what planet this happens on these people, likely downtrodden and ground under the bootheel of the feudalistic system, will follow their messiah, who is controlled by the BG, on a wave of violence.
Thus the BG will achieve power, or at the very least re-structure all of society to their whims. The highest goal would be to have the KH under their control placed on the throne. Now, this is where I see Paul as a victim of fate. Because of who he was, how he was bred, his mother' choice and the Emperor's command for Atreides to control Arrakis, he fit right into the whole BG design, unwittingly, like a puzzle piece. Which then leads us to him, in Cave of the Birds, realizing the Jihad is a foregone conclusion unless he somehow kills himself, Stilgar, Chani, his mom and everyone else present. Which, of course, Noble Paul is not willing to die, and is forced to ride a roller coaster of human suffering ending with him dying on the steps of the temple in Arrakeen, 21 years later.
