Pope St. Leo II (682-683) was the Pope who received the Acta of the 6th Ecumenical Council held in Constantinople in 681. As you all know, this is the Council which posthumously condemned Pope Honorius with the anathema due to heretics. Leo II ratified the Council and made no content of what the Council decided. When St. Leo II wrote to the Church of Spain to notify her King, Ervigius, of the Council and the anathema of monotheletism, the Pope begins his letter by announcing the intention of Christ in the Church for the proclamation of the truth. He writes:
“The savior of the world, the son of God, established this too, even among his holy disciples, when he established Peter as the prince of his disciples 𝑖𝑛 ℎ𝑖𝑠 𝑠𝑡𝑒𝑎𝑑 (𝐬𝐮𝐢 𝐯𝐢𝐜𝐞). By his saving preaching and transmission of his teaching, this whole apostolic church of Christ has been led, as if proceeding from the source, by his preaching; all the places over which your high rank presides [have been led] to the knowledge of truth and life, as the peak of your reign illustrates.”
Latin – Hoc etiam et in sanctis suis discipulis salvator mundi Dei Filius esse constituit, qui beatum Petrum sui vice discipulorum suorum instituit principem, cujus salutari praedicatione atque traditione ab hac cuncta apostolica Christi ecclesia… PL 96.418 (link)
That sounds like St. Leo is speaking of Christ intending to single out Peter as his “Vicar” (literally as speaking “in his stead”) for the purpose of maintaining a witness for the truth of the Apostolic tradition, even so late as in 7th century Spain through the ministry of the Roman see. Further along he tells the King that “𝑤𝑒 [the Roman Pontiffs] 𝑓𝑖𝑙𝑙 𝑡ℎ𝑒 𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛𝑒𝑑 𝑚𝑖𝑛𝑖𝑠𝑡𝑟𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑙𝑒𝑠𝑠𝑒𝑑 𝑃𝑒𝑡𝑒𝑟, 𝑝𝑟𝑖𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝐴𝑝𝑜𝑠𝑡𝑙𝑒𝑠, 𝑎𝑙𝑡ℎ𝑜𝑢𝑔ℎ 𝑤𝑒 𝑎𝑟𝑒 𝑢𝑛𝑒𝑞𝑢𝑎𝑙 [to the task].”
Very clearly, St. Leo II understands the Roman Pontiffs to be the heirs of St. Peter and his divinely established office as the “Vicar of Christ”.
However, in the same letter, he throws one of his predecessors under the same anathema, namely, Honorius:
“But the most pious emperor [Constantine IV], inspired by the grace of the Holy Spirit and undertaking the job of his own free will on behalf of the purity of the Christian faith, has striven to purify the catholic church of God from the stain of heretical error with utmost effort, and he caused to be removed from the midst of the church of God whatever offense could spring forth among Christian people. And ever inventory of a heretical statement who was condemned by the 𝒗𝒆𝒏𝒆𝒓𝒂𝒃𝒍𝒆 𝒄𝒐𝒖𝒏𝒄𝒊𝒍’𝒔 𝒋𝒖𝒅𝒈𝒎𝒆𝒏𝒕 was thrown out of the union of the catholic church: namely, Theodore, bishop of Pharan, Cyrus of Alexandria, Sergius, Paul; Pyrrhus and Peter, former Patriarchs of Constantinople; 𝒂𝒏𝒅 𝒕𝒐𝒈𝒆𝒕𝒉𝒆𝒓 𝒘𝒊𝒕𝒉 𝒕𝒉𝒆𝒎 𝒕𝒉𝒆 𝑹𝒐𝒎𝒂𝒏 𝑯𝒐𝒏𝒐𝒓𝒊𝒖𝒔, 𝒘𝒉𝒐 𝒂𝒈𝒓𝒆𝒆𝒅 𝒕𝒉𝒂𝒕 𝒕𝒉𝒆 𝒊𝒎𝒎𝒂𝒄𝒖𝒍𝒂𝒕𝒆 𝒓𝒖𝒍𝒆 𝒐𝒇 𝒂𝒑𝒐𝒔𝒕𝒐𝒍𝒊𝒄 𝒕𝒓𝒂𝒅𝒊𝒕𝒊𝒐𝒏 𝒘𝒉𝒊𝒄𝒉 𝒉𝒆 𝒓𝒆𝒄𝒆𝒊𝒗𝒆𝒅 𝒇𝒓𝒐𝒎 𝒉𝒊𝒔 𝒑𝒓𝒆𝒅𝒆𝒄𝒆𝒔𝒔𝒐𝒓 𝒃𝒆 𝒄𝒐𝒏𝒕𝒂𝒎𝒊𝒏𝒂𝒕𝒆𝒅; but also Macarius of Antioch with his disciple Stephn, or rather his teacher in heretical wickedness; and a certain Polychronius, a crazy old man, a new Simon [Magus], who lately was promising to end his reliance on heretical preaching, but again becoming confused, did not wish to be converted to the path of true confession, salvation, [and] was punished with eternal condemnation.”
Source – Patrologia Latina 96.418-420; Eng. Trans. Bronwen Neil & Pauline Allen, Conflict & Negotiation in the Early Church: Letters from Late Antiquity, trans. from the Greek, Latin, and Syriac (Washington, D.C.: The Catholic University of America Press, 2020), 235-38.
Therefore, this 7th century Roman Pontiff clearly held the following matters as factual:
(1) The Lord Jesus Christ divinely appointed St. Peter alone to be his “vicar” (i.e., in his stead) for the purpose of maintaining a “true confession” (Neil & Allen, p. 235) in the Church.
(2) The Roman Pontiff fills the commissioned position of St. Peter, which means the office of the Roman Pontiff is that which is the vicar of Christ by lawful succession.
(3) And yet, despite (1) and (2), a valid Roman Pontiff could publicly “contaminate” the faith and fall under the anathema for heresy, as well as be excommunicated from the Church by a Council ratified by a Pope (himself).
This is of enormous interest in light of the fact that Pope St. Agatho, at the 6th Ecumenical Council, staked the promise of Christ to Peter on the fact that none of the Roman Pontiffs ever turned away from the purity of the faith. A century prior, Pope St. Hormisdas (515) said that the promise of Christ (Mt 16) was proven by the fact that in the Apostolic See, the “catholic religion has always been upheld unsullied (without blemish).” That kind of standard is extremely high. How many errors and in how many modes does it take to bring a Church down? It took the homilies of Nestorius to contaminate the See of Constantinople. And yet, here, in 682, a Roman Pontiff comes out and says that a lawful successor of Peter can and did contaminate the faith, and thereby “pollute” (as he says elsewhere) the purity of the Apostolic See.