Usually I find articles from Bonocore here. AAARg. I once saw a "timeline" he had a hand in which claimed that Theodosius gave the title EP as a counter to Gratian giving the title pontif to the Pope of Rome. A glaring anachronism for starters.
This is article isn't too bad. Of course, it has its inadequacies.
He mentions that St. Gregory talks of Constantinople having heresiarchs. This of course was before Pope Honorius (who of course isnt' mentioned).
Of course it is interesting so much emphasis on the title, whereas in substance, the Vatican indeed only has one bishop.
Another thing sidestepped and not mentioned in the article is that St. Gregory during this cotroversy wrote that the patriarchs of Rome, Alexandria (through St. Mark) and Antioch are all one Petrine See. I've yet to see an explanation, then why Antioch shouldn't be ahead of Alexandria, since Antioch is Petrine directly, Alexandria second hand. Could it be because that was the secular order within the empire, like the Fathers alluded to in Constantinople c. 3 and Chalcedon c. 28 (btw, St. Gregory is quite wrong on the Pope's veto power: even Pope St. Leo recognized that his own bishops were not following his veto of canon 28)?

I always love this quote:
"As regards the Church of Constantinople,WHO CAN DOUBT THAT IT IS SUBJECT TO THE APOSTOLIC SEE? Why, both our Most Religious Lord the Emperor, and
our brother the Bishop of Constantinople, continually acknowledge it."
So the brother bishop of Constantinople, a/k/a the percursor of antichrist, continually acknowleges Rome. I've never seen the antichrist cited as a Church Father for papap supremacy outside of a Chick tract.