Where is the evidence for that belief? And I'm not talking about the obvious "reformers", because it seems to me you are claiming that contemporaries of St. Irenaeus, and later, all the way up to the "Reformation" (not just starting with it), were saying he was wrong about the supremacy of the Church of Rome. So where is the evidence for that, as Claud asked, where are the ECF's writings that demonstrate that that notion was prevailant, and popular, as you suggest, a good 1000 years before the "Reformation"?
He quotes the exact words of Marcion and Valentinus and other heretics as proof of what he says that they believe. He doesn't ask the reader to take his word for it. He cites their exact words from their "written documents".
Yet when it comes to telling us that Peter and Paul ordained the Church of Rome with superiority, he cites neither Peter nor Paul nor any other apostle. He cites no "written document" as evidence. The reader is supposed to take his word for this outlandish claim.
On the one hand he accuses the heretics of resorting to "tradition" or "viva voce" in lieu of the truth of the "written documents", and then resorts to the same thing himself.
Is it possible that the reason that he cites no source for his claim of superiority of the Church of Rome is because there was none and he knew it? The absence of any "written documentation" for his claim in light of what he had said in that regard of the heretics, goes to the heart of the lack of any substantive credibility for that claim.