Why be good?

[Randy Carson]

So we agree that people thought there had been such a Peter, over a hundred years before any of that was written...

Ignatius wrote within 50 years of that...not 100.

How come there's no other record of him at Rome... say... by some roman contemporary record-keeper?

There is. Read on.

First, Peter says in 1 Peter 5:13, "She who is at Babylon, who is likewise chosen, sends you greetings; and so does my son Mark." “Babylon” was an early Christian reference for “Rome,” so Peter and Mark are sending their greetings from Rome (not from the ancient city of Babylon).

Second, this is also the testimony of the Church Fathers, who testify that Mark is Peter's disciple and interpreter in Rome. St. Irenaeus, writing c. 180 A.D., says:

Matthew also issued a written Gospel among the Hebrews in their own dialect, while Peter and Paul were preaching at Rome, and laying the foundations of the Church. After their departure, Mark, the disciple and interpreter of Peter, did also hand down to us in writing what had been preached by Peter.

Eusebius says the same thing, as does St. Jerome:

Mark, the disciple and interpreter of Peter wrote a short gospel at the request of the brethren at Rome embodying what he had heard Peter tell. When Peter had heard this, he approved it and published it to the churches to be read by his authority as Clemens in the sixth book of his Hypotyposes and Papias, bishop of Hierapolis, record. Peter also mentions this Mark in his first epistle, figuratively indicating Rome under the name of Babylon "She who is in Babylon elect together with you salutes you and so does Mark my son." So, taking the gospel which he himself composed, he went to Egypt and first preaching Christ at Alexandria he formed a church so admirable in doctrine and continence of living that he constrained all followers of Christ to his example.

This makes Mark's Gospel all the more powerful: he's declaring that Jesus, not Caesar, is the true Son of God, and he is doing this from the heart of the Roman Empire.

Now consider this: Rufus, the son of Simon of Cyrene, was a Christian living in Rome. So was Simon's wife. We know this from a seemingly throwaway line in St. Paul's Epistle to the Romans,  "Greet Rufus, chosen in the Lord, and his mother, who has been a mother to me, too." (Rom. 16:13)

This explains why Mark would choose to mention that Simon of Cyrene was the father of Rufus and Alexander: those wouldn't have been random names to his original readers, but actual people that they knew. This detail is significant for several reasons.

First, it's another indication of the historicity of the Gospel: anyone doubting the veracity of Mark's account could go ask Rufus and Alexander.

Second, it shows unintended internal evidence for historical reliability of the New Testament accounts: by comparing multiple sources (Mark and Paul), a more coherent picture emerges. IOW, the writers are unintentionally supporting the overall gospel story because their stories frequently dovetail like this.

Finally, it points to something momentous and beautiful: Simon of Cyrene's encounter with Jesus the Cross brought about his conversion and the conversion of his whole family.