So (again, if my understanding is correct) there are three different approaches within the same Lutheran confession. Can someone explain from a Lutheran point of view why these three difference stances?
For reasons already stated by others, Luther himself regarded the episcopacy as superfluous, similar to Wesley’s ultimate conclusion that the bishop is not an order unto itself but merely an “office” within the presbyterate. (Compare Catholic views of the office of the Papacy within the universal episcopate). In this understanding, the bishop’s only function was to maintain order in the local churches and ensure the teaching of sound doctrine. In the caesaropapist tendencies of the Lutheran reformation, Luther accorded the “summus episcopus,” that is the episcopal duties of oversight and administration, to the territorial prince. Thus, as an example, in the Evangelical Church of Saxony, once subject to (I believe?) the bishops of the Province of Magdeburg, the dioceses were suppressed and the oversight exercised by the Prince-Elector of Saxony.
The princes usually left matters of doctrine to the theologians of the various universities, but every once in a while would intervene. The most (in)famous example was when the Prussian King Frederick William III, mandated that all the Lutheran and Reformed (Calvinist) congregations in his kingdom be merged into a single church body with a common order of service in 1817. This was especially offensive to Lutherans who believed that Calvinists profaned the Lord’s Supper. Someone correct me if I’m wrong, but I believe the exodus of many unyielding Lutherans was one of the origins of the founding of the Lutheran Church - Missouri Synod in the US.
This arrangement persisted in Germany until the collapse of the German Empire and its constituent kingdoms/principalities/etc in 1919. Only then, deprived of the territorial prince, did the various churches today comprising the Evangelical Church of Germany re-adopt episcopacy, as a “republican” alternative to the former caesaropapism. Though note that this bishops were an entirely modern creation, having no ordinal links to pre-Reformation bishops, so their “invalid” status in Rome’s eyes is a given.
There were some bishops who converted to Lutheranism, including a couple Prince-Archbishops of Cologne. So had the German Lutherans wished to maintain the Apostolic Succession in the sense understood by Catholics they easily could have, but they didn’t.
Scandinavia was a little different because the bishops had long since been “nationalized” in the sense that the dioceses of the Danish bishops were coterminous with the country of Denmark, etc. In Germany the bishops, outside the bounds of a territory and sometimes even a rival prince in their own right, could be viewed as a “foreign” interloper by a prince. In Scandinavia, however, the bishops had long occupied the usual place as advisors and administrators to the monarch. Thus the Scandinavian kings felt no need to discard with the episcopate and in fact viewed it as a useful institution for executing their intended religious reform.
A key difference was how it came about. When Christian III of Denmark-Norway instituted the Lutheran reform in his lands (including Iceland and Greenland besides the two kingdoms of Denmark and Norway) he at first adopted Luther’s view and completely abolished the episcopate. All the existing Catholic bishops either accepted the decree and retired from public life, fled to Catholic parts of Europe, or were imprisoned before ultimately choosing one of the first two options. Christian recognized the need for “executive officers” for his summus episcopus and established an office of “superintendant” to replace the bishops. These men, however, were just Lutheran theologians appointed by the king and had no ordinal ties to the pre-Reformation bishops. Later, to make the new officers more palatable to the people, who remained nostalgic for old forms, the superintendants were renamed “bishops” as they continue to this day. Needless to say, their orders would be “invalid” as far as Rome is concerned.
In Sweden, however, the Reformation came very differently. Sweden had been united to Denmark-Norway since 1397 in the “Union of Kalmar” and in 1523 a Swedish noble named Gustavus Vasa led a national revolt to re-establish Sweden as an independent country. Driving out the Danes, Gustavus was troubled in his efforts by the fact that the Catholic Archbishop of Uppsala was a Danish loyalist. He petitioned Pope Clement VII to replace the Archbishop with a new one more agreeable to Swedish independence. In what seems a blunder in hindsight, the Pope refused because he was hoping to keep the King of Denmark happy and thus keep Denmark in the Catholic Church. Gustavus Vasa surprised everyone when his revolution became permanent, and resenting Rome’s answer to his call for help, went on to adopt Lutheranism in Sweden as one of his first major acts as King Gustavus I. The Swedish reform was pretty conservative and maintained all the existing Catholic bishops who would agree to the reform in their sees. Additionally, when the king appointed his new Archbishop of Uppsala, Laurentius Petri, Petri was consecrated by another Swedish bishop who had been consecrated in Rome, allegedly by the Pope himself. This line of bishops continues to this day.
So if any Lutheran bishops were to be considered “valid” according to the Roman definition, then it would be those of the Swedish and Finnish Churches. But, given the low priority Lutherans place on the matter, neither the Swedes nor the Finns have ever bothered to inquire for Rome’s opinion on the matter.