“Problematic” is an interesting word choice. From a doctrinal perspective I don’t think it is problematic, because I don’t think the patriarchates, as ecclesiastical positions, are connected to Catholic doctrine at all. At various times in Church history, patriarchates have been added, and I suppose they could be removed. In the Catholic Church there are currently 15 bishops who bear the title “Patriarch,” including a patriarch of Venice and a patriarch of the East Indies.
Like the position of “monsignor,” I think the patriarchates are ecclesiastical positions that can be changed or modified as necessary. Unless I’ve misunderstood something, the pope could even abolish the position of “patriarch” today if he wanted to, in the same way he recently
announced that there would be no more monsignors.
From a perspective of historical nicety, I think it is either negative or positive that there are three Catholic patriarchs of Antioch, depending on how you look at it. On the negative side, it reflects the schisms that have affected Catholic history in the Antiochene church. On the positive side, it reminds us of the missions that converted large bodies of Christians back to the faith. These ancient sees had gone into schism first with Rome and then with each other until there were three major divisions in the Antiochene Church, but the Church went to great lengths to achieve unity. The Church allowed three distinct bodies of the faithful to maintain a bishop with the title “patriarch of Antioch” so long as they returned to the bosom of their Lord. To me, that is an impressive testament to the value the Church places on unity above historical nicety.
Let there be six hundred patriarchs of Antioch if it will save one more soul.
I hope that helps. God bless!