You cannot state that categorically.
See Letter to the Corinthians (Clement), Chapters 43 and 51. A challenge to the primacy of Aaron is seen as "sedition against Moses", and papacy is seen as prefigured in Aaron.
“...and papacy is seen as prefigured in Aaron.”
Where do you see that, Alex? +Clement doesn’t say that. No Father does.
That's a stretch. He was making a case for all priesthood, not just for Petrine (papal) authority. Deposing of bishops by the people of God is not unheard of in the Church and even Cyprian at one time argued for it, and it is not considered sedition.
The Church as a whole never compared the Pope/Bishop of Rome to Moses. Neither does the priesthood of the Apostolic Church parallel that of Judaism. The authority of the Apostles was delegated by Jesus to his 11 disciples (Mat 28:19) and they, in turn, delegated it to their successors, and they to theirs until today.
Judaic priesthood was assigned to the whole tribe and is inherited as birthright. There is no comparison to apsotolic authority and ordination.