I don't doubt that Peter may have traveled to Rome. I also don't doubt that Peter may have help Paul estblish some churches in Rome. All of this is, of course, speculation built on hearsay of church fathers. But that doesn't matter. What you have to establish is that Peter actually ruled from Rome as head of the Church in a Pope-like capacity. You will find the church fathers to be silent about this since up until the 4th century many of the churches ruled themselves. And, while Peter was adored by the fathers, the biblical evidence indicates that James was head of the Jerusalem Council-not Peter.
It is interesting in my mind that the second Pope after the dead of Peter was not John as one would naturally suppose since he was the last living Apostle. Rather (if memory serves me correctly) it was Linus. Why didn't the Church elect the last apostle to be Pope?
BTW-With the seven churches listen in Revelations, who's failings was it? The Church who commanded them?
“Our Lord, whose precepts and admonitions we ought to observe, describing the honour of a bishop and the order of His Church, speaks in the Gospel, and says to Peter: ‘I say unto thee, That thou art Peter, and upon this rock will I build my Church; and the gates of hell shall not prevail against it. And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shall loose on earth shall be loosed in heaven.’ Thence, through the changes of times and successions, the ordering of bishops and the PLAN OF THE CHURCH flow onwards; so that the Church is founded upon the bishops, and every act of the Church is controlled by these same rulers.” Cyprian, To the Lapsed, 1 (A.D. 250).
BTW,Dear Brother. This is before the 4th century
“”It is interesting in my mind that the second Pope after the dead of Peter was not John as one would naturally suppose since he was the last living Apostle. Rather (if memory serves me correctly) it was Linus. Why didn’t the Church elect the last apostle to be Pope?””
“And that you may still be more confident, that repenting thus truly there remains for you a sure hope of salvation, listen to a tale? Which is not a tale but a narrative, handed down and committed to the custody of memory, about the Apostle John. For when, on the tyrant’s death, he returned to Ephesus from the isle of Patmos, he went away, being invited, to the contiguous territories of the nations, here to appoint bishops, there to set in order whole Churches, there to ordain such as were marked out by the Spirit.” Clement of Alexandria, Who is the rich man that shall be save?, 42 (A.D. 210).
So you see... Saint John certainly played an important role in the Church.Perhaps more important then being Pope