When we examine the reasons for the abolition of the Papacy this becomes clear. If Simon Peter’s sole resume item for the job of first Pope is on the Matthew 16:18-19 passages “And I say unto you, that thou art Peter, and upon this rock I will build my church and the gates of Hell shall not prevail against it. I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven." then the Papacy case is thin to invisible. But, scriptural vagary and ambiguity of translation is only the first crack in the case for an authentic Papacy.
That the Roman Catholic Church has entered its epoch of weakness and contraction is beyond serious question. That this epoch of weakness will spiral down to the dissolution of the Papacy is no longer in doubt. That the regionalization of the Catholic Church following the pattern of Protestant denominations is the only logical outcome.
Catholics believe that God will always be with the Church "even to the end of time". That may be true, but that does not mean the Church must be centralized in Rome under the rule of a single monarch of a city/state. The Papacy is not the Church. The ways of the Divine are hidden and mysterious. They are embedded in the structure and function of Reality, Truth, Goodness, and Beauty.
The Papacy we know today began through a temporal power vacuum in Rome with the pontificate of Miltiades (311-314 A.D.). The Papacy was never officially voted by any Church Council, but rather, simply acknowledged by temporal princes, notably Emperor Constantine who gave the Lateran Palace to Miltiades then Bishop of Rome. Geography, politics, and the need for central administration of the early Catholic Church established the Papacy not scripture or even plenary councils. Hence, what was established by geography, politics and administrative need can be undone by those very same human forces. Since there is no further need for the geographical primacy of Rome, nor the political power of its bishop, nor the need for central administration in the digital age, then the Papacy should be abolished.
More to the point is the politics of ‘The Bishop of Rome’ incongruously evolving into ‘The Supreme Pontiff’ the global Catholic universe through political and economic intrigue among warring secular Princes, Kings, and Emperors. Saint Peter was hardly a ‘bishop’ of anything, let alone Rome. He spent most of his time hiding from the Emperors executioner’s until he was finally crucified, upside-down, so legend has it, at a date and time still uncertain. He was simply the leader of the first Christian sect, but certainly not a Pontifex Maximus as Popes later appropriated this ‘Chief-Priest’ title from pagan Roman religion. His successor, officially listed as Pope Linus I (67-76 AD) by Church historians actually did some ‘episcopal’ things like ordain priests and designate 25 parishes in and around Rome itself. But he was merely an administrator not anointed with the dogmatic ‘infallibility’ later crypto-Popes claimed. It would take several centuries for the term ‘Pope’ to be used in anything like its modern context.
Not until around 232 AD did the term refer to a Bishop and it was not to the Bishop of Rome. The first appearance of the term in modern context was used to refer to a Patriarch (Chief-Bishop), Patriarch of Alexandria, Pope Heraclas of Alexandria. The term ‘Pope’ (Latin: papa from Greek: πάππας pappas, an endearing word for "father") also known as the pontiff,(bridge) is the Bishop of Rome, and therefore ex officio the leader of the worldwide Catholic Church. It wasn’t until 325 AD at the First Council of Nicaea that its Sixth Canon hinted at the ‘special status’ of the Bishops of Rome, Alexandria, and Antioch. Hardly a mandate for ‘Papal Infallibility’ on matters of faith and dogma. Not until the fall of the Western Roman Empire in 476 did a major potentate, Clovis I King of the Francs, ally himself with the Bishop of Rome thus conferring tenuous primacy on that prelate above the other Bishops of the Catholics.
Only three Popes, Leo the Great: AD 440-461, Gregory the Great: AD 590-604, and Gregory VII: AD1015-1085 expanded temporal and political papal power from the simple ‘Bishop of Rome’ into: His Holiness , Vicar of Jesus Christ, Prince of the Apostles, Supreme Pontiff, Primate of Italy , Archbishop and Metropolitan of the Roman Province, Sovereign of the Vatican City State, and Servant of the servants of God. None of these vainglorious titles are consistent with the humble carpenter’s son from Nazareth named Jesus Christ.