That's basing our understanding of ministry on the Roman concept of "valid orders". The Divines taught that bishops are not of the esse but of the bene esse. St. Paul speaks of temporal government, not bishops. The Articles explain that each national church orders itself accordingly. In England that was bishops, in Scotland presbyteries, in Germany superintendents (which were accepted as "bishops" by Laud, without succession). The Fathers are great, but they are not Scripture. We can't hold something that Scripture does not hold as necessary. You have a very Tractarian concept of authority and ministry.