I stated the “permanence” of head bishop. Not denying leadership role of Peter . What you don’t have in scriptures is his passing the batton to sole successor, and such designation for he did ordain presbyters.
Have you had your will read yet?
Why not? Oh, because you are still alive!
Scripture (besides the fact that not every truth must appear in scripture) doesn’t record St. Peter’s death, so why would it record the passing of the batton, to use your words?
However, the ECF record just such a thing.
Clement of Rome
Our Apostles knew through our Lord Jesus Christ that there would be strife for the office of bishop. For this reason, therefore, having received perfect foreknowledge, they appointed those who have already been mentioned, and afterwards added the further provision that, if they should die, other approved men should succeed to their ministry (Letter to the Corinthians 44:1 [A.D. 95]).
Ignatius of Antioch
You must all follow the bishop as Jesus Christ follows the Father, and the presbytery as you would the Apostles. Reverence the deacons as you would the command of God. Let no one do anything of concern to the Church without the bishop. Let that be considered a valid Eucharist which is celebrated by the bishop, or by one whom he appoints. Wherever the bishop appears, let the people be there; just as wherever Jesus Christ is, there is the Catholic Church (Letter to the Smyrnaeans 8:1 [A.D. 110]).
Irenaeus
It is possible, then, for everyone in every Church, who may wish to know the truth, to contemplate the tradition of the Apostles which has been made known throughout the whole world. And we are in a position to enumerate those who were instituted bishops by the Apostles, and their successors to our own times: men who neither knew nor taught anything like these heretics rave about. For if the Apostles had known hidden mysteries which they taught to the elite secretly and apart from the rest, they would have handed them down especially to those very ones to whom they were committing the self-same Churches. For surely they wished all those and their successors to be perfect and without reproach, to whom they handed on their authority (Against Heresies 3:3:1 [A.D. 180-199]).
It is necessary to obey those who are the presbyters in the Church, those who, as we have shown, have succession from the Apostles; those who have received, with the succession of the episcopate, the sure charism of truth according to the good pleasure of the Father. But the rest, who have no part in the primitive succession and assemble wheresoever they will, must be held in suspicion (ibid 4:26:2).