Actually thinking about it more, in RBY and FRLG, Red never really stays as Champion. If you go back and fight E4 again, Blue is still there as Champion. So I guess if the Champion leaves then the previous Champion takes over. Which then explains why Lance is the Champion again in GSC, since Blue left to be a gym leader.
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[NO BARKLEY NO PEACE]
If you can't slam with the best, then jam with the rest.