The emperors rather then the Church eventually triumphing in the Investiture Controversy could have led somewhere, though more likely to a stronger and more unified HRE, as mentioned previously, than a unified Germany as such. The viewpoint of the emperors, often neglected due to the "obvious" justice of the Church making its own appointments, was that the major bishops and abbots were great temporal lords (and, whisper it, mainly functioned as such) as well as spiritual leaders, and important imperial counsellors, so it was right for the imperium to have a say in their appointments.
The Church however as it so often did dressed up a political power-grab in spiritual clothing. It didn't invariably win but on this occasion was successful, to the great weakening of imperial authority. Reverse that and the Empire in general and Germany in particular might never have fragmented to the same extent. Italy can be divested later, to give a more wholly German character to the Empire. Which I do regard as legitimately holding the title in addition to the Eastern Empire. There was even a former capital of the Western Empire on German soil, Trier. For sentiment's sake, that could be the choice for the capital of the eventual new Germany.
