Yes, note also in Paul’s letter to the Romans. Supposedly, Peter would have been the bishop there for many years and still would be when Paul wrote the letter, went there and was imprisoned. Not one mention of Peter ever, no greetings to him anywhere. And no help from him either if he was there!
Rome is a strange place.
And because the majority of the Apostles are never mentioned outside the Gospels, apparently they did NOTHING after Jesus rose from the dead. We have evidence that Peter was in Rome outside of the Scriptures. The majority of scholars also see "Babylon" as a code word for Rome, which would match what John writes in Revelation.
Really, yours is not a very good argument. The Bible doesn't say much about Hadrian's Wall, either, and there it stands...
Regards