I can see why you might read it like that, but it's just a consequence of the form. The idea is that galactic conflict is so large it's only representable in a dramatic way via a smaller structure like family. Maybe you'd object less if the family is someone other than the Skywalkers? I was wondering if the villain might come from Han Solo's family? Perhaps they forced him to join the Imperial academy because they were true believers and his rebellion began by becoming a smuggler? He might have some brother carrying on in the totalitarian footsteps of his father.