Many commentators, especially in recent years, have noted that Isa 22:21-23 plays an important background to Matt 16:18-19. LDS scholar Matthew Bowen wrote the following about the role of the Isa 22:21-23 and the promise Jesus gives to Peter at Caesarea Philippi:
The “Keys of the Kingdom”: Priesthood Keys and Power as Aspects of the Eternal Bedrock
Jesus’s surnaming of Peter was an important part of his priesthood leadership training. Peter was to become the model for all future apostolic and priesthood leadership. Hebrews 7:24 describes Christ’s authority as an “unchangeable priesthood,” based on Psalm 110, an enthronement psalm in which the Davidic king receives the Melchizedek priesthood eternally with an oath and covenant. Isaiah similarly envisages the investiture of the political and priesthood authority of the Davidic king in Eliakim, son of Hilkiah, a servant of Hezekiah, evidently the royal treasurer:
And I will clothe him with thy robe, and strengthen him with thy girdle, and I will commit thy government into his hand: and he shall be a father to the inhabitants of Jerusalem, and to the house of Judah. And the key of the house of David will I lay upon his shoulder; so he shall open, and none shall shut and he shall shut, and none shall open. And I will fasten him as a nail in a sure place [ûtěqa’tȋw yātēd běmāqôm ne’ěmān] and he shall be for a glorious throne to his father’s house. (Isaiah 22:21-23, emphasis added)
Similar to the Lord’s investiture of Eliakim, Jesus invests Peter with his (Jesus’s) own royal/priestly authority (the Melchizedek Priesthood authority). After the events detailed in Matthew 16-17 and 28, Peter is fully authorized to act in the Savior’s stead. After Jesus’s resurrection, Peter continued faithfully in this surrogate role until he himself apparently like the Savior, was “fasten[ed] . . . as a nail in a sure place.” Even after his death, in the spirit world and after his resurrection, Peter continued to operate in this role in building the church into a “sure house” against which “the gates of hell cannot prevail, thus fulfilling Isaiah’s prophecy that Zion would eventually become “tabernacle that shall not be taken down; not one of the stakes [yětēdōtâw = “its nails”] thereof shall ever be removed, neither shall any of the cords thereof be broken” (Isaiah 33:20; cf. 54:2; Moroni 10:31). (Matthew L. Bowen, Name as Key-Word: Collected Essays on Onomastic Wordplay and the Temple in Mormon Scripture [Salt Lake City: The Interpreter Foundation and Eborn Books, 2018], 282)