In hindsight, it makes perfect sense that Biden would be the first major player to go down.
Obama and Hillary are both cultural icons, like it or not. They are both extremely well-insulated, and media darlings. You can't "start" with such figures. The disbelief coupled with the widespread cover-up would be insurmountable.
Joe Biden, on the other hand, is NOT a beloved figure. In fact, he has never polled strongly outside of Delaware– which is the corporate epicenter of America. (tax shelter) He is a lifelong politician, with no real accomplishments, and has never been considered an intellectual, or a man of high character. Nor has he ever been the orator that Obama or Bill Clinton were.
In fact, Biden is perhaps the best example of a caricature of a corrupt DC politician. And being a dim-wit, he struggles mightily to defend himself, or deflect/pivot in the face of scandal. (He ends up coming off as an arrogant asshole.)
Joe Biden is the perfect choice to be the first domino to fall. The fact that he was a central figure in the Obama administration makes it that much more delicious.
What a great movie!