Films about corrupt politicians, dictators, etc.

Bravo, I don't think of A FACE IN THE CROWD as being about politicians, per se, although I do remember some political shenanigans of some kind in it (it's been a while since I've seen it). And the media and politics certainly seem to go together, especially today, don't they? That film was so ahead of its time in that regard! Didn't see AMERICAN HUSTLE or WHITE LIGHTENING so can't comment on those, but I love Ned Beatty.

And a clarification about CITIZEN KANE: it's a fictionalized portrayal of William Randolph Hearst, not the Getty family (if I understood you correctly). It was Hearst who refused to allow his newspapers to post any ads for the film, which probably kept it from being more successful than it might have been.