The Epistle to the Romans (ch. 1)

I suspect that the pre-conversion Saul visited Rome at some point of his life.  He his well-educated, articulate, and sophisticated.  I am not aware if he says whether he did or not in any New Testament book.

However, post-conversion Paul longs to visit the church in Rome during his missionary voyages.  He believes that God will take him there, so he writes an epistle to the Roman church.  This epistle is famously dense and is almost intimidating to write about.  So, what I write will seem superficial.

In chapter 1, Paul talks about these introductory remarks then launches into a discussion of the Christian faith.  It does not seem that this epistle was prompted by a problem with the Roman church, but Paul just has a lot to say to them.

One thing that stands out to me is that Paul mentions he was prevented from going to Rome.  Looking ahead in the Bible and to non-canonical sources, we know that Paul was later in house arrest in Rome and was likely executed there.

This is totally my own conjecture, but I suspect that God had a plan for both Paul and Peter to finish their time on earth in Rome to oversee the succession of the church from the foundational Apostles to people who never knew Christ on earth.  The "second Pope" is said to be Linus, who might be referred to in 2 Timothy 4.  At this time, the church in Rome was no more important than any other church, other than the fact it was the capital of the Empire.

But God, looking ahead centuries later knew that Emperor Constantine would convert to Christianity, which then put the emphasis on the church in Rome.  So, by moving Paul and Peter to Rome, the Roman church became a quasi-capital of the church while Peter and Paul could monitor the succession of the Roman church.

This is all my conjecture.  Likewise, I am not a Catholic, but I do think this is what happened.