They are not in the Executive Branch. We are talking about the temporary administration of the Executive Branch and NOT succession to the presidency.

Separation of powers! The Legislative cannot run the Executive and so on.

"Article XXX. In the government of this commonwealth, the legislative department shall never exercise the executive and judicial powers, or either of them: the executive shall never exercise the legislative and judicial powers, or either of them: the judicial shall never exercise the legislative and executive powers, or either of them: to the end it may be a government of laws and not of men."

I know, that's the Massachusetts Constitution, written by John Adams and ratified in 1780. But it gives you an idea of the separation of powers intended by the Founders.