Even then, there is a huge problem with the quote by Pope Innocent because he confirms that all bishops are the successors of Peter, claiming that the episcopacy flows from Peter.
Problematic too is that some of the quotes have no context and are heavily edited. Look for example at the quote written by St. Jerome. Notice how some of it has been cut out?
Here is a fuller version of the same quote: And yet John, one of the disciples, who is related to have been the youngest of the Apostles, and who was a virgin when he embraced Christianity, remained a virgin, and on that account was more beloved by our Lord, and lay upon the breast of Jesus. And what Peter, who had had a wife, did not dare ask, John
13:25 he requested John to ask. And after the resurrection, when Mary Magdalene told them that the Lord had risen, John20:4 they both ran to the sepulchre, but John outran Peter. And when they were fishing in the ship on the lake of Gennesaret, Jesus stood upon the shore, and the Apostles knew not who it was they saw; the virgin alone recognized a virgin, and said to Peter, It is the Lord. Again, after hearing the prediction that he must be bound by another, and led whither he would not, and must suffer on the cross, Peter said, Lord what shall this man do? being unwilling to desert John, with whom he had always been united. Our Lord said to him, What is that to you if I wish him so to be? Whence the saying went abroad among the brethren that that disciple should not die. Here we have a proof that virginity does not die, and that the defilement of marriage is not washed away by the blood of martyrdom, but virginity abides with Christ, and its sleep is not death but a passing to another state. If, however, Jovinianus should obstinately contend that John was not a virgin, (whereas we have maintained that his virginity was the cause of the special love our Lord bore to him), let him explain, if he was not a virgin, why it was that he was loved more than the other Apostles.
But you say, Matthew*16:18 the Church was founded upon Peter: although elsewhere the same is attributed to all the Apostles, and they all receive the keys of the kingdom of heaven, and the strength of the Church depends upon them all alike, yet one among the twelve is chosen so that when a head has been appointed, there may be no occasion for schism. But why was not John chosen, who was a virgin? Deference was paid to age, because Peter was the elder: one who was a youth, I may say almost a boy, could not be set over men of advanced age; and a good master who was bound to remove every occasion of strife among his disciples, and who had said to them, John*14:27 Peace I leave with you, my peace I give unto you, and, He that is the greater among you, let him be the least of all, would not be thought to afford cause of envy against the youth whom he had loved. We maybe sure that John was then a boy because ecclesiastical history most clearly proves that he lived to the reign of Trajan, that is, he fell asleep in the sixty-eighth year after our Lordās passion, as I have briefly noted in my treatise on Illustrious Men. Peter is an Apostle, and John is an Apostleā the one a married man, the other a virgin; but Peter is an Apostle only, John is both an Apostle and an Evangelist, and a prophet. An Apostle, because he wrote to the Churches as a master; an Evangelist, because he composed a Gospel, a thing which no other of the Apostles, excepting Matthew, did; a prophet, for he saw in the island of Patmos, to which he had been banished by the Emperor Domitian as a martyr for the Lord, an Apocalypse containing the boundless mysteries of the future.
newadvent.org/fathers/30091.htm Shockingly, in this passage, St. Jerome is arguing that virginity is better, because St. John, a virgin, was the most-beloved of the apostles by the Lord. He then goes on to argue that even though Peter was appointed head, this was only for good order and because Peter was the oldest of the apostles. He even says that all of the apostles were given the keys! He then goes on to show how much more special John the apostle and evangelist is than Peter, who is merely an apostle. Look then at how dishonestly that quotation was edited, when in fact, it says just the opposite of what it was edited to say. How many of those other quotations then, perhaps say something else other than what they have been edited to say?