The problem with the historical argument is that in the N.T., you cannot even be a church member if you live in unrepentant, willful sin, which so many popes did, let alone be a pastor. Thus these cannot qualify as successors to Peter, nor is an office filled based upon genealogical pedigree. I addition, the utter lack of any plans or procedure for selecting a future new pope, and perpetuating his office, like as was carefully provided for replacing Judas, is most conspicuous, as major doctrines need such. But what we are given are the qualification for bishops/elders (same office).
As for Mt. 16, see a prior past, and i can gt back to that later if need be.
Well, let me see some verses.
Which first 200 popes, who were killed, lived in unrepented sin?
Why were the authorities so bent on killing the "non-leaders" of the Catholic Church?
200 = ca. 20