Some of the Fathers assumed Isaiah 22 in discussing the keys. Irenaeus, Origen, and Jerome all referred to Jesus as “the one who holds the key of David.” They received this image from Revelation 3:7, but Rev. 3:7 directly quotes Isaiah 22:22. Scholars as profound as Irenaeus. Origen and Jerome certainly knew about the Davidic background of Matthew 16:18, but they approached the question from a different angle than we do today. They assumed what we question: namely, that authority can and must be passed on from generation to generation. Therefore, they were not faced with the necessity (as we are) of “proving” that Jesus passed His authority on to Peter, and Peter to his successors. To them, it was natural and inevitable that Jesus would do so. They were much more interested in the consequences that flowed from that passing on of authority, and they saw the auhtority the keys symbolize as a gift not just to Peter and his generation, but to the entire Church for all time.

Hope this helps!

Carl