Were Ephesus and Constantinople prominent because of a perpetual office instituted by Jesus or the apostles?

Because none of the earliest Christian sources refer to a papacy, Catholics often resort to suggesting that any sort of reference to a prominence or primacy of the Roman church is adequate evidence for the office. But when sources like Paul, Ignatius, Dionysius of Corinth, Irenaeus, and Tertullian commend the Roman church for non-papal reasons, it doesn't make sense to equate that with affirming that the Roman bishop has papal authority. It's sometimes suggested that critics of Catholicism are asking for too much when they make that sort of distinction. But it does make sense to distinguish between two concepts that aren't the same, and we do that with other early churches and early bishops. Think of how prominent churches other than Rome were in early church history (Jerusalem in the book of Acts, Ignatius' comments about the significance of the church of Ephesus, what Irenaeus said about the importance of the churches of Ephesus and Smyrna, the prominence of Constantinople in later centuries, etc.). All that Protestants and other critics of Roman Catholicism are doing is applying the same reasoning to Rome that we and Roman Catholics apply to other churches.