St. Peter was not the first bishop of Rome. He was the first apostle of the Ebionite sect.
Bishop Linus may have been the first bishop of Rome but he was ordained by Paul - which actually means that he may have been Marcionite. But since we know that Marcion sent a woman missionary to Rome named Marcellina who helped to establish a sect similar to Marcionism known as Carpocrations, I think it more likely that Linus was a Carpocration.
With all the talk lately about the Bible vs the Pope I think the current (Catholic) New Testament canon should be given a proper perspective. Rome attempted to create a unified Christian sect by combining Marcionism and Ebionism - and this is what is really meant by saying that Rome was founded by both Peter and Paul, i.e. by both Ebionites and Marcionites. Accordingly, the Bible canon is a combination of Ebionite and Marcionite scriptures.
I think it was a mistake to attempt the union of the Ebionite and Marcionite sects. There are numerous contradictions between these two sects and accordingly there were numerous alterations to various books in the Bible in an effort to harmonize the contradictions between the scriptures of the two groups which were incorporated in the Bible canon.
---- To begin with Acts did NOT follow Luke nor were they of the same author. This was a harmonization alteration effort. You see, Luke was of Marcionite origin and the Acts of the Apostles was of Ebionite origin. Both books were altered to create a false harmonization of the two sects: Marcionism and Ebionism via their scriptures.
The Baptism of Jesus was not native to either Mark of Matthew, but came from the Ebionite Gospel called the Gospel of the Hebrews. This was one of the differences between the Ebionites and the Marcionites - The Baptism of Jesus was central to the Ebionites, but denied by the Marcionites - note how the Gospel of Luke (which came from the Marcionite Gospel of the Lord) makes no mention of the Baptism of Jesus except for a very short interpolation; which, by the way (and this is actually a very important point) makes no mention of the baptizer: John!
I know there are many who wish to be "Bible-only" dogmatic Christians believing that the Holy Spirit somehow keeps those books in the Catholic canon of scripture from error. But which books in the Bible are inspired? Are the ones that came from the Ebionites the ones, or are the ones from the Marcionites the ones which are inspired? Are the Catholic corrected/harmonized versions the correct ones? - if so that means that the Catholic editors are the ones who were the inspired ones!
Maybe one should ask the question if the Holy Spirit really protects the integrity of scripture! When Moses tossed the tablets containing the ten commandments written by god's own hands, why did the Holy Spirit allow them to be broken and lost?