This is not a forum for an exegetical discussion like what you suggest.
But the short answer is this.
“Christian generations do not exist as self contained islands. It is the same Church, whether we are talking about the first century, or the twentieth. Its essential character and activities persist. Peter’s ministry is as much a part of its life now as it was and has always been throughout its history the Church will need its rock; it will need to be strengthened, and it will need to be fed.” (Fr. Roderick Strange, The Catholic Faith, Oxford University Press).
Actually, it is fit for any such, but all i am asking are some basic questions here. .
But the short answer is this. “Christian generations do not exist as self contained islands....
That is simply not an answer to my question, unless you mean that the basis for your assurance that Rome is the one true church, with its (conditionally) infallible magisterium, is that it is necessary. And perhaps the historicity and tradition of Rome and promises of Scripture give you full assurance that she is that infallible church.
Is that the basis for your assurance, and why do we need that infallible church?
Big snowstorm here today, so i may be typing and shoveling!