Let's not forget that there are many Eastern Orthodox Churches, too. Not all of them are in communion, either. But that is a beautiful thought; you are obviously using your heart! The Eastern Orthodox, Oriental Orthodox, and Assyrian Church of the East are all churches of valid apostolic succession, so in theory, all of their bishops, archimandrites, monastics, and any other celibate clergy I might have left out would all be eligible to be the Bishop of Rome. I know we've had multiple African Popes, and I think we HAVE had multiple Eastern Popes as well. I love that story about ancient Rome...that's really cool.
I think the first thing an Eastern Orthodox Pope would try to do would be to declare ex cathedra
that Popes don't have the authority to make infallible doctrines and reverse those infallible doctrines already promulgated.
Wouldn't that be a paradox! In theory, I guess the Holy Spirit would stop him or something...if He didn't, that would like...undo the universe.
BTW there's already an Eastern Pope. The Orthodox Patriarch of Alexandria is actually properly referred to as a "Pope" as well. Their current Pope is Pope Shenouda III. He's just the Patriarch of the Coptic Church (like our Pope is the Patriarch of Rome); he doesn't claim authority over any other church. I hear he and JP2 are good friends, but I only know that as a rumor, not a fact.