Do you see how you argue from all points as long as you perceive that you are correct?
First you place the idea of “Pope” on the 6th century; then you argue against a markedly earlier use of the term as inconsequential because it is not found in the mouth of the Apostles… all the while rejecting what is not found in the mouth of Jesus or the Apostles as proof that the Church is organic and she has grown from her infancy with Doctrinal Practices and Norms Unfolded by the Holy Spirit.
I liken arguments as yours as those of the ‘scholars’ and ‘theologians’ who claimed that John’s Gospel invented things till, by chance, truth was unearthed… or the ones who claim that there were no real miracles but exaggerations made to make Jesus seem more ‘Divine.’ These often put away the Divinity and argue on pure human science and abilities…
…as for the ‘unbiased student of Sacred Scripture,’ the problem with that premise is that there is bias as we cannot help but end up discovering the ‘proof’ of our preconceptions–unless we allow the Holy Spirit to truly be our Guide in Unfolding and Understand God’s Salvific Plan, which includes the Church (a Church) which is the Body of Christ:
1 I therefore, a prisoner in the Lord, beseech you that you walk worthy of the vocation in which you are called, 2 With all humility and mildness, with patience, supporting one another in charity. 3 Careful to keep the unity of the Spirit in the bond of peace. 4 One body and one Spirit; as you are called in one hope of your calling. 5 One Lord, one faith, one baptism. 6 One God and Father of all, who is above all, and through all, and in us all. (Ephesians 4)