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I think that there were only four members and no Champion when Blue battled the Elite Four, but he wasn't the very first Champion. I think it more likely that the previous Champion either died or retired, so there was nobody holding the position of Champion until Blue took it.
I'd say the positions of Elite Four members and other professional trainers are only reorganized when there is a significant change in the "rankings" of trainers, such as a trainer becoming the new Champion. Since Red arrived immediately after Blue there was no time to discuss what changes, if any, needed to be made to the League positions. However, by the time of Gen II there had been plenty of time for necessary changes to be made.
