JL: I suggest the reason is because they recognize Rome as the see of Peter. And no other Apostolic church could seriously claim to be Universal Pastor. Only one was given the keys.
BZzzzt!
Wrong.
Other Apostolic churches do not have a theory of one unique human individual running the universal church. There never was a central administration of the church, not even in St Peter’s day.
If the eastern churches had a Pope-like authority, when there were schisms they would have propose one of their own to do the job. Not one change was made to eastern church governance, not one new canon was written, to account for a loss of a ‘Pope’.
This has only happened in the west, when there were two contending Roman Catholic churches, then three. Each had their own Pope, and each Pope had his own cardinals. They did not know how to function without one, and when there was uncertainty about who was the legitimate sole head of the church, the church split.
Obviously this was because by the 13th century the western churches had adopted the notion that they
needed to have a Pope who ruled all the churches. The local synods in the west had lost their autocephaly, and the ability to govern themselves.
Papacy is not part of the collective experience of orthodoxy. It was not present at the time of the Chalcedonian controversy, because the pre-Chalcedonians (Oriental Orthodox to Roman Catholics) did not inherit such a tradition.
It was not present in the 11th century because the Byzantines and their associated churches did not inherit such a tradition.
Both communions are running fine, just as they did before the separations.
Papacy, ie Roman Ultramontanist Papacy, did not exist in the early church, and never existed in the east. It is a completely western phenomenon, a unique theory which is unfamiliar to Apostolic Christianity.
Eastern Christian churches have a synodal form of government, and this has always been the way it works from the days pre-Edict of Milan. This was also the way the western churches governed themselves until the local synods in the west were suppressed.