If you are correct above, then why is St. Peter mentioned the most times in the Gospels and Acts of the Apostles? Just for kicks?
Saint Paul wrote most of the New Testament, and he wasn't "just for kicks" either. So, what, shall we say that Paul was "Pope"?
No, of course not. While both Saints Peter and Paul (and all the Apostles, to arguably somewhat lesser extents) had critically important roles to play in the EXTENSION of the Biblical Church, the Biblically-Established Form of Church Government was Conciliar, not Papal.
We can see this clearly in Acts 15, where the Presiding Apostle James (NOT PETER) "pronounces judgment" (Acts 15:19) for the Whole Church, but only according to the CONCILIAR CONSENSUS of the Whole Church (Acts 15:22).