OP-
Eph 5:23 KJV - 23 For the husband is the head of the wife, even as Christ is the head of the church: and he is the saviour of the body.
So isn't it disingenuous to refer to Linus as the first "Pope"? Or would he in fact have consciously been incorporated into an existing organization that ruled the church universal?
It does not particularly matter whether the bishop of Rome named Linus is or is not the same as the one mentioned in Paul's letter to Timothy.
Nor does it matter whether the Clement mentioned is the same Clement who followed in Linus' footsteps.
What is important is whether at that time of Linus circa CE 68 to 78 did the church at Rome consider herself to be the head of the Body of Christ and thus would its bishop consider himself to also be the head?
The answer is no Linus did not. We know this because he is sandwiched between Paul's admonition in Eph 5:23 quoted above and Clement's assertion shown next. Clement reigned in Rome circa CE 88 to 99. Between them was Anacletus. Again the dates and persons do not matter as much as what they left in writing.
Let us then, men and brethren, with all energy act the part of soldiers, in accordance with His holy commandments.
-Clement Letter-
In other words, at that time the church at Rome still taught and believed as Paul had instructed. Christ is the head and we are His soldiers.
We find similar thoughts in Clement's next chapters. Christ is the head and we are all of His body.
Let our whole body, then, be preserved in Christ Jesus; and let every one be subject to his neighbour...
-ibid-chapter XXXVIII
And then there's this in chapter XLII.
The apostles have preached the Gospel to us from the Lord Jesus Christ; Jesus Christ [has done so] from God. Christ therefore was sent forth by God, and the apostles by Christ. Both these appointments, then, were made in an orderly way, according to the will of God. Having therefore received their orders, and being fully assured by the resurrection of our Lord Jesus Christ, and established in the word of God, with full assurance of the Holy Ghost, they went forth proclaiming that the kingdom of God was at hand. And thus preaching through countries and cities, they appointed the first-fruits [of their labours], having first proved them by the Spirit, to be bishops and deacons of those who should afterwards believe.
There is no sense from Clement of some hierarchy in the church on the earth among the churches. The head is Christ.
There is, however, a sense of order of bishop and deacon and believer, but again there is no sense that one earthly bishop is necessarily above another bishop in a different location. Christ appointed apostles who went out. They all appointed the first-fruits, the second generation of those faithful men who would teach the same apostolic teaching everywhere.
So, according to the church at Rome at the time of Linus, there was no sense that Linus was a pope over all churches or the head of the church on earth.
Subsequently, perhaps even as early as Sixtus I reign a mere 30 years later and certainly by Pope Victor circa CE 195, there was the beginnings of the Papal System.