I apologise for the all caps. *cringe*
My reasoning is fairly basic - the people elect a President trusting his
or her (who are we kidding?) judgement in choosing his successor - the Vice-President. In the event that the Vice Presidency's vacant it makes sense that the President's successor should also be chosen by him, hence a member of the Cabinet.
Furthermore, a member of the President's Cabinet is more likely to be closer to his philosophy and ideology than is the PPT - who could be any random Senator, meaning that Atlasians would be more likely to get an executive that's closely aligned with the views and outlook of the departing President.
And, yeah, I think we can all agree we can't afford some freak incident where Yankee becomes President and leaves the Senate.