Because those who use it have obviously read John's book and are using his terminology.
And how do you know that Peter didn't already use it? Christians were largely underground at the time; they would have needed to misdirect any Roman inquisitors away from overt criticism of the Empire.
How come Paul does not use this code name for Rome for his writings from and to Rome? And what about Luke and the others? How come they didn't use that code name?
Peter was a straight-forward apostle who would and did speak his mind and told things just as they were --- without fear and deception.
If you assume that it was a code name, then where is the decoding book? How about "Mark" --- maybe that is a code word for someone else. And "Peace" might be a code word too.
What other words in the NT letters were code words that didn't mean what they said?
It's not obvious to me. How do you arrive at your conclusions?
We have a documented and agreed upon code word in the New Testament - Babylon for Rome. We are not discussing any others which may or may not exist. The charge has been made that Peter was nevef in Rome. We have evidence that he was.
I understand that there is a great desire to discredit Peter as having the primacy, and thus by so doing they attempt to deny that he was the first Pope, and therefore the Catholic claim of Apostolic Succession would fall apart. By denying Apostolic Succession they would then try to show that the Catholic Church is not the Church which Jesus Christ founded. It isn't going to happen, but the great desire is there in some measure as justification for all the split-off churches. If the Catholic Church turns out to be founded by men, then that lets some of the pressure off all those whose churches really were founded by men.
The Emperor Claudius (Acts 18:2) tries to get rid of all Jews from Rome. If Babylon is the code word for Rome, then this conclusion is actually more justified Scripturally than yours is. Is it possible that the Roman Catholic Church is much more Bible based than are the Bible-based Protestants? It would seem so, given that we have the entire Bible, not an abridged version; we have never eliminated any of the Old Testament and we have never changed the intent of any of Sacred Scripture. It seems that modern Christian sects are given to hysterical attitudes that concentrate on producing ever new interpretations of these millennia-old verses.