“In neither his nor Paul’s letters is there any indication that Peter was ever in Rome.”
An argument from silence - a great fallacy commited by many protestants.
Even if he was brought there for execution, the fact remains that he never served there. The false claim that Peter was the first pope is appropriately labeled, “Fiction, pure and simple”
If he indeed was not in Rome than explain this (this is just a selection):
Dionysius of Corinth
“You have also, by your very admonition, brought together the planting that was made by Peter and Paul at Rome and at Corinth; for both of them alike planted in our Corinth and taught us; and both alike, teaching similarly in Italy, suffered martyrdom at the same time” (Letter to Soter of Rome [inter A.D. 166 -174] recorded by Eusebius).
Irenaeus
Matthew also issued among the Hebrews a written Gospel in their own language, while Peter and Paul were evangelizing in Rome and laying the foundation of the Church. After their departure, Mark, the disciple and interpreter of Peter, also handed down to us in writing what had been preached by Peter (Against Heresies 3:1:1 [A.D. 189]).
But since it would be too long to enumerate in such a volume as this the successions of all the Churches, we shall confound all those who, in whatever manner, whether through self-satisfaction or vainglory, or through blindness and wicked opinion, assemble other than where it is proper, by pointing out here the successions of the bishops of the greatest and most ancient Church known to all, founded and organized at Rome by the two most glorious Apostles, Peter and Paul, that Church which has the tradition and the faith which comes down to us after having been announced to men by the Apostles. For with this Church, because of its superior origin, all Churches must agree, that is, all the faithful in the whole world; and it is in her that the faithful everywhere have maintained the Apostolic tradition (Against Heresies 3:3:2 [A.D. 189]).
Tertullian
Let us see what milk the Corinthians drained from Paul; against what standard the Galatians were measured for correction; what the Philippians, Thessalonians, and Ephesians read; what even the nearby Romans sound forth, to whom both Peter and Paul bequeathed the Gospel and even sealed it with their blood (Against Marcion 4:5:1 [inter A.D. 207-212]).
Eusebius
The Apostle Peter, after he has established the Church in Antioch, is sent to Rome, where he remains bishop of that city, preaching the Gospel for twenty-five years (The Chronicle, Ad An. Dom. 42 [A.D. 303]).
When Peter preached the Word publicly at Rome, and declared the Gospel by the Spirit, many who were present requested that Mark, who had been for a long time his follower and who remembered his sayings, should write down what had been proclaimed. Having composed the Gospel, he gave it to those who had requested it (Ecclesiastical History 6:14:1 [A.D. 325]).
Peter of Alexandria
Peter, the first chosen of the Apostles, having been apprehended often and thrown into prison and treated with ignominy, at last was crucified in Rome (Canonical Letter, canon 9 [A.D. 306]).
