If it can't be proven that Peter was in Rome then all that after that can't fall into place and brings into question that Peter was the first Pope and any further succession. BTW, who was Pope after Peter?
Yes, that's that argument is a classic anti-Catholic argument to attempt to debunk the papacy, even when proof to the contrary is given.
Linus was the second Pope; we know that he knew Paul, because he is mentioned in 2 Tim. 4:21. He was followed by Cletus, who was followed by Clement (mentioned in Phil 4:3)... and so it goes.
By the way, you do realize that this has NOTHING to do with the topic of this thread?