Would the Holy Roman Emperor for example accepted that his Church (the German Archbishoprics/Bishoprics) to be subordinate to the nearest Pope/Patriarch (in this case it might be Milan) who can claim Apostolic foundation?
The King of Germany wouldn't accept this, that's why I'm postulating an alliance between the Bishop of Rome and the King of Germany, exchanging the Imperial Crown and Papal blessing for German support of making real Roman claims of religious supremacy.
Since OTL the Kings of Germany (and later Holy Roman Emperors of the German Nation) battled for centuries for control of Northern Italy. I see an alliance between the King of Germany (who wants to break the power of Lombard City-States) and the Bishop of Rome (who wants to break the power of the pretender-Patriarch of Milan) as natural. In this alliance, I don't think the King of Germany would be giving up any control that he exercises over the German Church, he is simply pledging the German Church's loyalty to the Bishop of Rome. Now later you may have conflicts, but with the history of a weak Papacy (the broken Church is going to be a big issue) I think a western version of Caesar-papism is the likely outcome.
I think that no King/Emperor would allow an outsider dictating his domestic policies... He might forge something to have one of his Archbishops elevated as Pope... Forgeries were a common thing in medieval times...
With the natural alliance I see between the Bishop of Rome and the King of Germany, I don't see this as becoming an issue. After all, by forgoing the forgery, the King of Germany can make a bid for Universal Empire, as the secular leader of Christiandom.
What is the time frame your looking at this for? Because if the Western Church breaks apart early, this is going to have very interesting effects on Western history. The breaking of the Western Church is probably going to quickly lead to schismatic theology, which will make reunification via council more difficult, and reunification via force more likely.
I really don't see the Western Church breaking this way, because I think the secular leadership lacked the kind of continuity and stability that I think was required to take on the very powerful organization the Church managed to develop.