Please see
here and
here for more evidence that Roman dominance at least is a product of later centuries.
As to episcopal supremacy, I would strongly suggest a contrasting look at three of the VERY earliest church fathers:
St. Ignatius of Antioch wrote passionately of the need to follow the bishop. He of course was a bishop with nearly monarchical power. St. Ignatius wrote his letters from himself.
St. Polycarp of Smyrna, on the other hand, was a bishop whose writings didn’t have such episcopal leadership behind it. He wrote his epistle to the Philippians, “Polycarp and the presbyters that are with him.” In fact, when Ignatius
wrote to Smyrna, he wrote to them “let nothing be done without the bishop.” If Polycarp was of the same mind, why did Ignatius need to tell the church in Smyrna?
We can also look at the letter from
St. Clement to the Corinthians, after they deposed their bishop and some of the priests. Clement of Rome (i.e., the bishop) used language that was not of command, but persuasion. Still, the Corinthians listened! So there’s definite suggestion that the Roman bishop had pull (though curiously, it doesn’t seem to suggest authority over the Corinthians). He does argue for the apostolic nature of bishops:
*"Our apostles also knew, through our Lord Jesus Christ, and there would be strife on account of the office of the episcopate. For this reason, therefore, inasmuch as they had obtained a perfect fore-knowledge of this, they appointed those [ministers] already mentioned, and afterwards gave instructions, that when these should fall asleep, other approved men should succeed them in their ministry. We are of opinion, therefore, that those appointed by them, or afterwards by other eminent men, with the consent of the whole Church, and who have blame-lessly served the flock of Christ in a humble, peaceable, and disinterested spirit, and have for a long time possessed the good opinion of all, cannot be justly dismissed from the ministry. For our sin will not be small, if we eject from the episcopate those who have blamelessly and holily fulfilled its duties. Blessed are those presbyters who, having finished their course before now, have obtained a fruitful and perfect departure [from this world]; for they have no fear lest any one deprive them of the place now appointed them. But we see that you have removed some men of excellent behaviour from the ministry, which they fulfilled blamelessly and with honour. "
*