Actually, the fact is that not only is Luther not a pope to us by a long shot (he was actually far more Catholic than us evangelical types), nor he did reject the teaching office established by God anymore than did "prophets and wise men, and scribes" (Mt. 23:34) which God raised up before him to reprove those who sat in power.
And Westminster states,
It belongeth to synods and councils [not as assuredly infallible but as a help in grace], ministerially, to determine controversies of faith, and cases of conscience; to set down rules and directions for the better ordering of the public worship of God, and government of his Church; to receive complaints in cases of maladministration, and authoritatively to determine the same:... (CHAPTER XXXI )
But not as a perpetually assuredly (conditionally) infallible office.
The fact is that the church began upon Scriptural substantiation in word and in power, as alone it is the supreme material standard for obedience and testing truth claims, as is abundantly evidenced . In contrast is that of a person or church decreeing that it alone is the supreme infallible interpreter.
It seems your argument is that an infallible (conditionally) magisterium is necessary as being the steward of Scripture which assuredly establishes what is of God, so that its judgment on what it rejects or affirms must be submitted to. And the veracity of which magisterium is the ordained means by which one has assurance of Truth.
And that historical descent shows Rome to be that infallible steward of Scripture. Is this what you are arguing?
As to the historic structure, which we see in East and West, whatever the cultural differences, the development of the papacy came about, if not of necessity than from the evident need for a place of appeal. As to Westminster, it is a bit ironic, since every Englishman, at that time, Catholic and Protestant, was convinced that Christian had more or less stated in England, what with Joseph of Arimathera, the Holy Grail and all that , taken on faith alone. If an English synod said, it it must be infallibly true. ;)