But note something very important. While Paul founded many churches, it was the churches that Peter founded which were the most important and authoritative "patriarchal" churches: Antioch and Rome (and even Alexandria, through Peter's disciple Mark). These Churches exercised a special primacy in their respective regions and went on to become the recognized seats of the three original Patriarchates.
Paul's churches had no such special patriarchal authority.
Where in scripture is there a necessity for "patriarchal authority" of one church over another, and where in scripture is such authority conferred?
A lot of man-made traditions have grown up within the Catholic church over the last 2000 years, and much of them have questionable validity, and much of them obscure the simplicity of the gospel of salvation through faith in Christ.