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.
It is not a stretch. The analogy to Aaron and Moses is an important part of the letter and its purpose is to establish the principle of there being an authority over other bishops.
It is true that the sacerdotal heredity in Christendom is spiritual and not biological like in Judaism, but that is also true of the Church replacing the ethnic community of Ancient Israel spiritually and not biologically.