Well, there's nothing in Scripture either that supports the primacy of Peter, nor does it at all address apostolic succession or how it's to be carried out, nor does it address the subsequent popes.
And many people have been martyred for their faith. How does them being martyred for their faith mean anything except that they were martyred for their faith?
the primacy of Peter was established by Christ...the future operations , successions,ruberiks,local rules, day by day operations, finances, charity giving, orphanages, hospitals, were pretty much left up to the Catholic church which had been assured that Christ would oversee until the end of time....and all this without error in faith and morals....pretty impressive I'd say.!!!