There is no suggestion I am aware of that the Papacy was meant to be a continuation of the Moses seat; and I can say with certainty that there is no evidence that the Bishop of Rome, or any other diocese, was ever a rotating position.
Huh? Only "Peter's seat" then(?) while otherwise there is reasonable enough consideration (and PLENTY of talk and "suggestion") of "the church" stretching not only back all the way to Moses, but through him also, back all the way to Abraham(!) else we loose our original moorings -- for those two men where in no wise cut off from the original branches of the Vine (who Christ testified He himself was).
Must that portion of your response be so wooden?
Part of the reason I brought mention of Caiaphas being used of the Lord to prophesy, is to highlight how the Lord will indeed utilize the office in spite of the lack of understanding and/or abundance of misunderstanding which any particular occupant may have --- which concept cannot but be also part of the contemplations which had been engaged in as part of the "faith" as it were that "the Church" be infallible in it's teachings, with the begging question there being always, at all times and instance -- "what and who precisely --- is the church?"
I suggest Tertullian in part, did provide answer;
What now? Are we to limit this to only those who have been questioned by certain and particular interrogators?
Tertullian himself included no such stipulations, which can result in the keys referenced being inheritable beyond those having qualified themselves in some form by having received ordinations from men.