“I just gave you an example of an important piece of patristic literature where a bishop of Rome corrects someone whom he accuses of sedition and implies Aaronic privilege.”
Alex, the writings of The Fathers are full of instances where a Patriarch or Metropolitan corrects other bishops. There is even the use of the story of Korah in those corrections and by the Patriarchs of Alexandria and Constantinople. The consensus patrum, it seems to me, is clear. The story is used to support hierarchial ecclesiology. The Fathers knew the story, Alex. Its clear they didn’t connect it to papal supremacy.
The implication, however, is there; it comes with the very idea of hierarchical leadership. I do not dispute that papal supremacy is a latter historical development; it would be as anachronistic for the Fathers to discuss it as, for example, discuss the use of electricity. What I am saying is that the concept of multiple autocephalic churches that absolutely, never-ever should have a hierarchical top is a later invention also.