Your list of the "other four" original Patriarchates (Churches) is ... wrong.
And the Chaldean Church is in communion with Rome, as are "Eastern" Churches throughout eastern Europe and Asia Minor.
And that Anglican Ordinariate was welcomed with great joy by the "Roman" Catholics on this forum.
There were a number of church centers, but the 5 that rose to prominency were the ones I listed and were the main movers and shakers at different points in history.
Rome was often consulted because it was distant from the other four and was hoped to be impartial. Doesn’t mean it was always agreed with.
However that lasted till Rome tried to assert Papal supremacy, and the Eastern Orthodox told him to spit up a rope to start the Great Schism which never has been healed but on paper.
The may get along and they may take communion, but I guarantee you historians from the other sects do not and will not agree on and do not accept Roman primacy, nor will they ever.
I have a feeling that brother Free Vulcan is repeating what he thinks Rome is about. We must as Catholics also emphasise that the Pope as Patriach of the West is equal to the other Patriarchs, not greater or lesser, but as per tradition, first among equals