Every Pope that I've heard of has been from the Latin rite/the Roman Catholic Church. Is it possible for the Pope to be a bishop from an Eastern Catholic church instead? For example I reckon it'd be really cool to have a Pope from the Syro-Malabar Church or the Ethiopian or Eritrean Churches, or the Byzantine Melkite Church.
I'm wondering if this has happened at any time historically and if not, why not? Is there anything preventing an Eastern Catholic bishop from being elected Pope?
If an Eastern bishop were to be elected Pope, could they celebrate their native liturgical rite regularly in Vatican City? Or would they be forced into using the Roman Rite most of the time? My understanding is that this is possible because the Pope is considered omniritual: he can celebrate whatever liturgy he wants and is not tied down to the Latin Rite.
As a historical footnote, I'll point out that before the great schism there was a period of church history where the Popes were all imported from Byzantine Greece, Byzantine Syria, and Byzantine Sicily. However this was before the great schism and so is not as remarkable as it seems at first glance because Eastern and Western Christianity were united at the time. See here: Byzantine Papacy