True. But President Kennedy asked the National Security Council for the correct procedure for replacing the government in the event of a surprise Soviet nuclear strike that took out the District of Columbia. The NSC said that the only body with the authority to choose a new president would be the Electoral College chosen in the last presidential election.
Senate vacancies are filled by the state governors.
Except in those states, like Massachusetts, where the new senator must be chosen in a special election.
OK, now that was prior to the 25th Amendment...