<< This certainly implies a visible unified Church with a leader (not mention that it is implied that the office will be filled when the current prime minister dies). >>
Changing the topic of the thread, but Yes it does:
In summarizing the above Protestant scholars (I cite M. Eugene Boring, Francis Wright Beare, Eduard Schweizer, R.T. France, Joachim Jeremias, George Arthur Buttrick, Willoughby C. Allen, and the Lutheran-Catholic study by Raymond Brown/John Reumann), the authority of the “keys” and the power of “binding and loosing” stand for the following –
(A) The keys of the kingdom represent authoritative teaching, and Peter’s role as holder of the keys is fulfilled now on earth as Christ’s chief teacher;
(B) The keeper of the keys, according to the background of Matthew 16:19, has authority within the house as administrator and teacher (cf. Isaiah 22);
© The authority of the keys is likened to that of the teachers of the Law in Jesus’ day, and the correct interpretation of the Law given by Jesus is accessible to the early community (the Church) through the tradition of Peter;
(D) The authority of the keys of the kingdom (Matt 16:19) are not different from the key of David (Isaiah 22:22; Rev 3:7), since Jesus controls and is in possession of both;
(E) Therefore, the keys (or “key” singular) represent FULL authorization, FULL authority, PLENARY authority, SUPREME authority;
(F) The keys of the kingdom are NOT to be understood as merely entrance keys (or “opening the door of faith” to the Gentiles), but rather to the bundle of keys carried by the chief steward who regulated the affairs of the entire household (cf. Isaiah 22), which in the New Covenant is Christ’s universal Church (cf. Matt 16:18; 1 Tim 3:15);
(G) Peter, as holder of the keys, is not merely the “gatekeeper of heaven” or “doorkeeper” but is therefore the Chief Steward of the Kingdom of Heaven (the Church) on earth;
(H) Further, the power of the keys can represent baptismal or penitential discipline, excommunication, exclusion from the Eucharist, legislative powers or the power of governing the affairs of the Church;
(I) The language of “binding” and “loosing” is Rabbinic terminology for authoritative teaching or a teaching function (or “Halakhic” pronouncements), denoting the authoritative declaration that an action is permitted or forbidden by the law of Moses, and in the Church the authority to pronounce judgment on unbelievers and promise forgiveness to believers;
(J) The “binding” and “loosing” refers to the Magisterium (the teaching authority of the early community, which Jesus was establishing through His apostles in His Church) to declare a commandment or teaching binding or not binding, forbidden or allowed, and God in heaven will ratify, seal, or confirm that decision made on earth (cf. Matthew 16:19; 18:18).
And further, The Anchor Bible commentary on Matthew by William F. Albright/C.S. Mann, the Evangelical New Bible Commentary, the Lutheran-Catholic study on Peter by Brown/Reumann, the Brethren/Mennonite commentary by Richard B. Gardner, and F.F. Bruce specifically connect Isaiah 22 to Matthew 16:
“And what about the ‘keys of the kingdom’ ? The keys of a royal or noble establishment were entrusted to the chief steward or majordomo [or “prime minister”]; he carried them on his shoulder in earlier times, and there they served as a badge of the authority entrusted to him. About 700 B.C. an oracle from God announced that this authority in the royal palace in Jerusalem was to be conferred on a man called Eliakim …(Isaiah 22:22). So in the new community which Jesus was about to build, Peter would be, so to speak, chief steward.” (Bruce, The Hard Sayings of Jesus [Intervarsity Press, 1983], 143-144, cited in Butler/Dahlgren/Hess, page 41)
Back on topic: Bible teaches Bible is sole rule of faith where?