In this case there must be clear BIBILICAL evidence since the churches at Jerusalem and Rome were contemporaneous. We know that Peter was at the church of Jerusalem (as the apostle to the "circumcision"). So if indeed God changed His plans and made him "THE bishop of Rome" (and apostle to the Gentiles), then Scripture would have brought this to light.
So what do we see in Paul's epistle to the Romans?
1. THE CHURCH AT ROME WAS A GENTILE CHURCH
Now I would not have you ignorant, brethren, that oftentimes I purposed to come unto you, (but was let [prevented] hitherto,) that I might have some fruit among you also, even as among other Gentiles. (Rom 1:13)
2. PAUL AS THE APOSTLE TO THE GENTILES WOULD GO TO THEM
Whensoever I take my journey into Spain, I will come to you: for I trust to see you in my journey, and to be brought on my way thitherward by you, if first I be somewhat filled with your company. (Rom 15:24)
3. PAUL SENT GREETINGS TO MORE THAN 29 CHRISTIANS, BUT PETER IS NOT MENTIONED -- AND THAT IS NOT ODD?.
The following Christians are commended or greeted in this epistle: Phebe, Priscilla and Aquila, Epaenetus, Mary, Andronicus and Junia, Amplias, Urbane, Stachys, Apelles, Aristobulus, Herodion, Narcissus, Tryphena and Tryphosa, Persis,
Rufus and his mother, Asyncritus, Phlegon, Hermas, Patrobas, Hermes, Philologus, Julia, Nereus, and his sister, and Olympas.