Undoutably geography could have played an important role. But I don't know if it did in fact play a center or pivotal role.
Perhaps most importantly from a military view point was the endless wars that ravaged Italy during this time. The Popes never really had troops they could use to begin with so all other considerations were ultimately moot. While the monarchies of France and Spain were willing to furnish troops for the Holy See, other states were not.
While the ability to move troops to enforce confomity was important. First you had to have the ability to get those troops into the area with the approval of the local nobility and royalty. In England thanks to a Pope stanging on principles and ex-communicating the king this wasn't going to happen. Likewise the long standing fued between the Papacy and the Holy Roman Empire limited options in Germany unless the local rules allowed papal troops or supporters in.