“...some vague and unsubstantiated genealogical claim of a Petrine Pedigree”?
Apostolic succession is not vague, illusionary or merely an artificial construct. It a divine assurance that we have an authentic authoritative claim to Christ’s teaching. After all, the Bible’s canon wasn’t finalized until 398 A.D. yet the Church was already active spreading the Gospel message as Christ had commanded and had gone through 15 Popes most of which were martyrs. Christ said that He would be with His Church for all time and that includes the 1500 years or so before Calvin. I can’t fathom why Christ would wait 1500 years until His correct doctrine for salvation would emerge?
And it is certainly not “unsubstantiated” although I am sure you would like it to be. Throwing stones at the 2000 year old Church will not bring it down. Now to answer the all important question, “Who has the authority?” In order to have only one truth, it is necessary to have only one authority. The truth cannot be divided up. St Augustine understood succession when he said,
“Before His suffering the Lord Jesus Christ, as you know, chose His disciples, whom He called Apostles. Among these Apostles almost everywhere Peter alone merited to represent the whole Church. For the sake of his representing the whole Church, which he alone could do, he merited to hear, I will give you the keys of the kingdom of Heaven (Matt 16:19).”
Sermons 295,2, 391 A.D.
“What they found in the Church they kept; what they learned, they taught; what they received from the fathers, they handed on to the sons.”
Against Julian, 2,10,33, 421 A.D.
Continuity is pretty important and it authenticates our beliefs. Saint Athanasius, in a letter to Serapion, 359 A.D., said ,”But what is also to the point, let us note that the very tradition, teaching and faith of the Catholic Church from the beginning, which the Lord gave, was preached by the Apostles, and was preserved by the Fathers. On this was the Church founded; and if anyone departs from this, he neither is nor any longer ought to be called a Christian.”
I consider that succinct and a clear validation of our faith.
1) I just reread 1 Corinthians 9 in it’s entirety, and it still looks to me like Paul is talking primarily about the ministry of the Gospel and the rewards associated with that as the basis for his personal discipline against his earthy appetites. The context is definitely not individual salvation. If you're convinced otherwise, make a detailed argument, but please don't ask me to accept a general assertion that totally ignores multiple obvious references to Paul's ministration of the Gospel and the rewards associated with that ministry.
2) I don't do genealogical arguments, and Petrine succession is precisely that, and necessarily so. I will instead direct you to a good discussion which I am relatively certain you will consider old hat. Be that as it may. I don’t do infinite loops either. I have a day job, after all. Perhaps when I retire … Anyway, here’s the site:
How Reliable Is Roman Catholic History?
3) I will address your point on authority. All Christians do have a single point of unified authority, the risen Jesus. He is not hypothetical, but more perfectly real than any institutional counterpart could ever be. Furthermore, he is not incompetent to administer and preserve his own church, and the idea that some human intermediary must be there to help him coalesce the exercise of authority in his church runs contrary to the risen Jesus pictured in the Apocalypse, as one who was busily rewarding some churches for their faithfulness and threatening others with dissolution, all without so much as a whisper of Peter's voice or office, but as something he was quite able to do on his own. Believers have no need for any master but Jesus (as he said), because His sheep will always hear his voice (as he said). Peace, SR