If you want to use “succeed” in the intransitive mode to express the meaning of “come next in line or succession, follow after another, replace another in an office or a position” then the correct preposition to use is “to”.
I would agree in the throne example, but not in the job example, at least not in American English. It just doens't sound right. He succeeded Peter Smith in that position, perhaps, meaning he held it immediately after Peter.
Companies do have succession planning, meaning who will take a key position if the person currently in theh position leaves, but you still would not say "Barbara will