Here Ignatius twice says how Rome “presides.” For this, he uses the Greek word “prokatthemena,” which is defined as an authoritative, jurisdictional position; and this is the meaning of the word whenever Ignatius uses it.
He also, later in the same letter, tells the church of Rome …
“You have never envied anyone,
you have taught others. Now I desire that those things may be confirmed [by your conduct], which in *
your instructions you enjoin [on others]. Only request in my behalf both inward and outward strength, that I may not only speak, but [truly] will; and that I may not merely be called a Christian, but really be found to be one.” (Ignatius to the Romans, Chap. III)
Here, Ignatius is asking the Romans not to interfere with his martyrdom or try to save his life as he is led to death in the Roman arena. But, in requesting this, Ignatius mentions how Rome is known for giving instructions to other churches and to be a teacher of others. This is precisely what we see in Clement, and in Ireneaus, and in Dionysius, and even in Tertullian above.
So, the patristic record is FAR from silent.

Rather, it is your side that lacks any evidence. And if you disagree, why don’t you show us some??
We never have one mention of a single bishop in charge of a city or a region.>>>>
Total nonsense. Read the Epistles of Ignatius of Antioch. Again, Ignatius was a CONTEMPORARY of Clement; and he NAMES the reigning bishops of Ephesus, Smyrna, Magnesia, Tralles, and Philadelphia. What’s more, in his epistle to the Ephesians, Ignatius makes this all-telling statement:
“…as also **bishops, settled everywhere to the utmost bounds [of the earth]****, are so by the will of Jesus Christ.” (Ignatius to the Ephesians Chap III).
As everyone knows, whenever Ignatius uses the word “bishop,” it always refers to the singular leader of a city-church; and he clearly says that such bishops exist EVERYWHERE …including Rome.
One reason, we still have the Biblically based system of multiple bishops, elders, presbyters, in charge of the churches at this time. >>>>>
That is total nonsense and an American Evangelical fabrication. Even in the Bible itself, there was always a leading presbyter (later exclusively called “bishop”) in each city-church who unified and presided over the presbyters …just as each synagogue had a chief rabbi among the other rabbis Don’t believe me?

Look at the evidence:
James was unquestionably the leading presbyter (read: bishop) of Jerusalem:
Acts 21:17-19: “When we reached Jerusalem the brothers welcomed us warmly. The next day, Paul accompanied us on a visit
to James, and all the presbyters were present. He greeted
them and proceeded to tell
them in detail what God had accomplished among the Gentiles through his ministry.”
Galatians 2:12: “For until some people came
from James*, he used to eat with the Gentiles …”
Similarly, Timothy held the office of monarchial leader in Ephesus. For, using the
singular “you” in Greek*, Paul instructs Timothy how to managing the Ephesian church, saying …
1 Tim 5:17-22 – “Presbyters who preside well deserve double honor …Do not accept (YOU singular) an accusation against a presbyter unless it is supported by two or three witnesses. Reprimand (YOU singular) publicly those who do sin, so that the rest also will be afraid. I charge YOU (singular) before God and Christ Jesus and the elect angels to keep these rules without prejudice, doing nothing out of favoritism. Do not lay hands (YOU singular) too readily on anyone …”
Therefore, Timothy himself was the one who both ordained presbyters and sat in judgment of them. He was the bishop.