There are those who contend that Peter was martyred at Rome. There is no evidence for this that comes anywhere near to satisfying the criteria of modern historians, who treat secondary evidence (and nothing better exists for this claim) according to the expected reliability of its authors.
Define the "primary source" evidence for the existence of Jesus Christ as taughtby the Christian Church, or corroborating evidence for the existence of these purported Apostles.
The earliest fragments of holy scripture date only to mid second century, and these self-same historians discount the authorship of the apostolic epistles.
The evidence for the apostolicity of the epistles and gospels are all secondary, ie the patristic accounts and historic references of, for example, Eusebius (who purports to have access to primitive documents which no longer exist).
IOW, the entire Christian enterprise rests on secondary sources- yet from what I have witnessed, you would arbitrarily and capriciously discount one secondary source over another. Bad form.
The naivete of the past has gone, and the "They would say that" test is now made. For this claim, in every case, the authors are suspect, having obvious vested interests, being often the survivors of persecution. In other words, the evidence in this case is as useful as a WW2 Nazi propaganda broadcast in identifying the close of WW2 action.
If Mt 16:18 was to be used as a basis for placing the church under imperial control (along with every other social entity in the Roman Empire- the church was never going to be an exception, if it survived at all) it was necessary to 'locate' Peter in Rome, where his 'successors' could remain under close control. As Peter's martyrdom was prophesied by Jesus, the logical course was to have his martyrdom chronicled in Rome. Peter was not a Roman citizen, was not apostle to Rome, was kept very busy from Anatolia to Persia, and there was no reason for him to go to Rome. It is unlikely that he ever went there, and if he did, it would never have been as a mere bishop or elder, one of many in that large city, and he could not have been the first bishop there anyway. Had he gone under Roman authority, he would never have been allowed contact with the church, and his existence in Rome would have been of no religious significance. Paul even wrote to apostles in Rome, so bishop Peter would have been under their authority! The Roman account of events and relationships, on all applicable counts, cannot be reconciled with Scripture, and it is no surprise whatever that, early in the Renaissance, independent readers of Scripture rejected it, and had to flee for their lives.
I don't see you here running for your life, so let's tone down the drama.
Regarding corroboration of Peter being at, martyred at, and being Bishop of Rome, a few sources:
St. Ignatius of Antioch (d. 107), who referred to the Church at Rome as "the Church of Peter and Paul" (Letter to the Romans)
St. Cyprian (d. 251), who described Rome as 'The place of Peter" (Epistle 520
St. Jerome (d. 420), who called Rome "the See of Peter" (Epistle 15, to Pope Damasus).
Around A.D. 166, Bishop Dionysius of Corinth wrote to Pope Soter, "You have also, by your very admonition, brought together the planting that was made by Peter and Paul at Rome
."(quoted in Eusebius, Ecclesiastical History, 2:25).
Now these same sources are of the type relied upon for the veracity and apostolicity of the New Testament.
Succession is anyway discounted by Peter, Jude and Paul in their letters, that explicitly warn of false teachers actually inside the church as they wrote.
Their warning about false teachers has absolutely nothing to do with succession, except in your fertile imagination.
The whole purpose of Christ's coming was to do away with external control as applied to Israel, and even the Israelites had no rulers intended for them, no bishops in the sense that Rome employed them. So it was utterly, deeply and fundamentally inimical to Christianity and Judaism to seek to create a hierarchy and associate it with Christianity.
Jesus as a social revolutionary- where have I read that? No interpretive bias on your part there, eh.
If Jesus was so bent on eliminating hierarchy, as you say, one wonders why He chose 12 and 72 and why these self-same went about selecting elders in every city.
Monarchical bishops were almost certainly devised by Roman emperors to facilitate the erosion of democracy in the church, and control by themselves, which is precisely what any historian would predict would happen, as night follows day. It is quite possible, even probable, that the imperial court had assistance and advice from former Sadducees and Pharisees, who feared Christians as much as corrupt, avaricious Roman patricians did.
I note the addition of your moderating term "monarchial." No latent bias evident there, eh.
Similar considerations regarding church polity apply to the notion that James was the first bishop of Jerusalem. This canard ignores the evidence in Acts that shows that the Jerusalem church was as democratic when advising Antioch as when it 'succeeded' Jesus Himself in replacing Judas.
You are ignoring the histoical practice of having bishops 'rule' over their own See (region). Therefore, the leadership of the Church, as practiced in the EO, is and was 'democratic (poor word choice- "collegiate" or "consensus" would be better descriptors).
Thus, your evidenciary argument is moot.
It is based on the flimsiest evidence, which fact is itself effectively self-contradictory. That 'evidence' is selective translation of a single word in Acts, which word has been otherwise accounted for here, but that alternative has been totally ignored.
There is no real debate here, only shouting and posturing. Nothing more need be said.
Thus endeth the strawman.
Note that I have not done any more shouting or posturing than you yourself, and much remains to be said, eg. sources for your historical redaction.