Gregory I (the great, 590 - 604 CE) did not set out to extend the political power of the Roman Church. Rather, it happened out of necessity. Unlike Pope Leo (or even Pelagius II) before him, Gregory was not in the position to exert or extend the power of the Roman See because of the Lombard threat to the north and because of the apparent benign neglect of the Imperial throne and Eastern Church. Gregory's hands were tied, as it were, because of the weakened state of Rome as he took the Throne of St. Peter. Rome had little chance to rise to her former greatness: frequent plagues, invasions, intense poverty and religious persecution (by the Arians) made sure of that. Gregory needed to make the lives of the Roman citizens worth living. They needed to be reminded of the coming Glory of the Church.
Gregory has been, therefore, misunderstood as a political reformer. He viewed Man as torn between two worlds: the active and contemplative. But unlike Augustine and Cassian before him, Gregory did not see these spheres as mutually exclusive (which would mean that political reformation would have some weight as an entity separate from theology). Instead, for Gregory, the reward of the active, public life is monastic and contemplative repose and leisure. Furthermore, the reward of contemplative leisure is a renewed vigor for and deeper understanding of active life.
In terms of politics, then, Gregory's "reforms" were not in the service of papal power or of the Church, but rather for religious faith itself. His active, public, political work was in fact an attempt to reap the reward for activity (contemplation) for Christendom (the eschatological fulfillment of the Church, the inauguration of the Heavenly Kingdom). Gregory felt that time was running out for humanity, and therefore Christendom needed a strong leader who would be able to fulfill the Church and bring about the End Times, which would in turn lead to an eternity of contemplation. That the result of his work was the creation of the Papal States and of the age of Church supremacy in Europe is merely a coincidence.
And, in terms of Medieval Studies as a discipline, it is a red herring.
When looked at from Gregory's perspective his reforms were far closer to that of Luther (another misunderstood reformer): Change the Church for the spiritual gain of Christendom. Laws, politics, expansion of empires, etc. have nothing to do with it at all. Gregory, like Luther, Augustine, Cassian et. al., was a theologian, not a politician. The attempt is to create a "long line of reformers" that ends with Gregory during the Early Church Period. While it is very neat and orderly to view it that way, it is not necessarily the story. In Gregory we have a rather anomalous figure who was far more concerned with faith than with politics.