True, the primacy of Rome would not have been mentioned, as the writing of Revelation (late first century) was about five hundred years before the Bishop of Rome exalted himself over all.
And consider the unholy unScriptural manner just one of the early movers in that direction worked to attain it, Pope Damasus 1, who is officially a Roman Catholic Church "saint.".
On Pope Liberius's death September 24 A.D. 366, violent disorders broke out over the choice of a successor. A group who had remained consistently loyal to Liberius immediately elected his deacon Ursinus in the Julian basilica and had him consecrated Bishop, but the rival faction of Felix's adherence elected Damasus, who did not hesitate to consolidate his claim by hiring a gang of thugs, storming the Julian Basilica in carrying out a three-day massacre of the Ursinians.
On Sunday, October 1 his partisans seized the Lateran Basilica, and he was there consecrated. He then sought the help of the city prefect (the first occasion of a Pope in enlisting the civil power against his adversaries), and he promptly expelled Ursinus and his followers from Rome. Mob violence continued until October 26, when Damasus's men attacked the Liberian Basilica, where the Ursinians had sought refuge; the pagan historian Ammianus Marcellinus reports that they left 137 dead on the field.
Damasus was now secure on his throne; but the bishops of Italy were shocked by the reports they received, and his moral authority was weakened for several years....
Damasus enjoy the favor of court and aristocracy,... His magnificent lifestyle and hospitality help to break down the anti-Christian prejudices of upper-class pagan families. He was active in repressing heresies, including Arianism, and did not scruple to call in the secular power... His measures against the intransigently Nicene disciples of Lucifer of Cagliari (d. 370/ 1) were particularly brutal...
Damasus was indefatigable in promoting the Roman primacy, frequently referring to Rome as 'the apostolic see' and ruling that the test of a creed's orthodoxy was its endorsement by the Pope.
In 378, he persuaded the government to recognize the holy see as a court of first instance and also of appeal for the Western episcopate... In tune with his ideas, Theodosius 1 (379-95) declared (February 27, 380) Christianity the state religion in that form from which the Romans had once [imagined they] received from St. Peter.. , This [false claim to] succession gave him a unique [presumptuous claim to] judicial power to bind and loose, and the assurance of this infused all his rulings on church discipline. -Kelly, J. N. D. (1989). The Oxford Dictionary of Popes. USA: Oxford University Press. pp. 32,34.