Well, the fragmentation did not begin with the Reformation. In Apostolic times,
Now this I say, that every one of you saith, I am of Paul; and I of Apollos; and I of Cephas; and I of Christ.1 Corinthians 1:12
Clearly, this is not the perfect will of God - but also clearly it is part of His permissive will. Only one of the current fragments of Christianity claims (but does not possess) infallible perfection - the rest of us realize that our doctrine is not perfect, but that does not stop the pursuit of doctrinal purity as a goal.
Although the papists tried to exterminate them, there were Christians living outside papal domination from the first century until the Reformation.
Clearly, this is not the perfect will of God - but also clearly it is part of His permissive will.
"Clearly" in what sense? There is not a single example of Christian congregations separated by anything but locale in the entire scripture.
Only one of the current fragments of Christianity claims (but does not possess) infallible perfection
Such a denial requires a demonstration of authority for making it.
Although the papists tried to exterminate them, there were Christians living outside papal domination from the first century until the Reformation.
Where does scripture authorize THAT claim?