Why does BSG's "Assign Vice President" card not affect succession?
The only mechanical effect I can see to this tweak is that a Cylon president could control who gets the presidency after they reveal, say if they know who the other unrevealed Cylon is.

If you need thematic justification for the original rule, I seem to remember an episode of the show where Zarek (when he was VP) told Roslin that he didn't want to be president.