CynicalBear:
Does it clearly state in the NT that Peter was in Rome. No, but does Babylon mean Rome as code or does it refer to the ancient city in what is modern day Iraq? That is the question. By NT times, Babylon was nothing of any sort and just an eastern outpost of the Roman empire. There were very few, if any Jews there, and very few Christians during the time the NT was being written.
Christianity and when God willed the incarnation, whether you want to admit it or not, came into the world and grew in the context of Roman-Greek culture. Rome was the center of the world and there is no Church Father, not one, starting with St. Papias [65 to 130 AD], St. CLement of ROme who wrote in 95AD, St. Ignatius of Antioch in 107 AD, St. Ireneaus of Lyon who wrote in 175 AD who does not state clearly and with no hesitation that Peter was in Rome.
For the record, the NT doesn’t say much about any of the Apostles and where they eventually went. The early Church [Fathers] though does attest to where the Apostles all went to preach and where they were eventually martyred [save the Apostle John, who went to an area near Ephesus where he took care of Mary the Mother of God and eventually died of natural causes].
The RCC also made up the ascension of Mary, so what? There goes their credibility.