Yes, it is an absurd stretch to think that Peter was in Babylon, Iraq, which had been long deserted, the fact that Jews may have persisted in Babylonia notwithstanding.
I know there’s a wierd school of Protestant apologetics which has to disbelieve everything Catholics and Orthodox believe, but Peter really did die just outside Rome, which he, like John, called Babylon. (In fact, the papacy refers to Rome as Babylon; the Vatican Hill was across the Tiber from the ancient city of Rome. The papacy resides in the Vatican so as to remain in exile from Babylon.)
Peter’s death in Rome was attested to by Clement, whom he named Bishop, in the first century. Peter’s actual burial place was found in a City of the Dead beneath the Vatican in 1942, complete with the inscription, “Here Lies Peter.”
It is clear that Peter's ministry was to the Circumcision, the Hebrews, whose main locus was in Mesopotamia with the main Talmud shul at Babylon, literally.
Paul wrote to the church at Rome in late AD 57/early 58, and if Peter were there, I would think among the many people in the church that he specifically named, Peter would have been one of them.
Peter's First General Epistle was written in the winter if 65-66, at the time Paul was in Macedonia.
In 68, Paul was again in Rome, and wrote to Timothy to come there and bring Mark with Him. Where was Peter then? Where was Mark? They were not in Rome, were they? If Mark was accompanying Peter, and Peter was in Antioch, probably Mark was with him. It seems much more likely they had come back from Babylon (near what is now Baghdad) after a stint trying to evangelize the Jewish population of the Mideast.
I do not think it is necessary to create a figurative location when the plain-literal will do just fine. The first and simplest rule of hermeneutics is "If the plain sense of a passage makes common sense, seek no other sense."
Peter wrote his Second General Epistle in the summer of 67, and Paul wrote again to Timothy from Rome in the spring of 68. Were they playing hide and seek with one another in Rome, or ignoring one another . . . or was it that simply their paths did not cross. And if that is true, Peter, at the time his epistles were written, he was elsewhere than Rome. In the first case, he, with Mark and Silvanus (=Silas, also known by Paul) were in Babylon.
I don't accept your "Babylon" = Rome hypothesis for this interpretation.
In fact, there is no Scriptural support whatsoever that Simon Peter was ever in Rome, actually, and plenty of evidence that he was situated in the geographic middle of his "see" throughout after leaving Jerusalem.
Are you being hyperbolic by saying this or do you really believe some "weird" school of Protestant apologists disbelieve "everything" Catholics and Orthodox believe? I have never heard of ANY "Christian" denomination that cannot find common ground on the very basics of Christianity with Catholics/Orthodox.
Going to Babylon (btw Dangus, while Babylon had been deserted in the 1st century, it was just across the river from Ctesiphon, the capital of the Parthians and from Seleucia (set up by Seleucid, a diadochi (companion) of Alexander the great) of which it was originally a suburb.
Other apostles went to the east, significantly St. Thomas who preached to the Jews in southern India (Jews had and have been there since the 5th century BC)
Peter did die just outside Rome -- as dangus correctly points out, the Vatican hill is not one of the seven hills of Rome and was outside the boundaries of the city even outside the Aurelian walls