It's a fun question, but there's an answer to it. Between the death of St. Peter and the death of St. John, we have the documentary evidence of 1 Clement (typically dated to either c. 68 or c. 96-97). In it, St. Clement begins: "The church of God which sojourns at Rome, to the church of God sojourning at Corinth, to them that are called and sanctified by the will of God, through our Lord Jesus Christ: Grace unto you, and peace, from Almighty God through Jesus Christ, be multiplied. Owing, dear brethren, to the sudden and successive calamitous events which have happened to ourselves, we feel that we have been somewhat tardy in turning our attention to the points respecting which you consulted us..." So you have here an epistle in which the pope (writing on behalf of the Church of Rome) not only addresses a controversy within Corinth, but does so *at their request.* IOW, they bypassed the Apostle John to write to Rome, and no one seems to have found it strange, or believed it was a usurpation.