I'd say ever since the Vatican was established, the papacy has been able to exercise a level of autonomy that it never held previously. I mean, first there were the 300 years where Christianity was illegal within the Roman Empire. Then, there was the period where it was legal, but had to contend with the emperors. After the Fall, it had to contend with the rise of the European kingdoms, such as Charlemagne's Frankish Empire. Once the Italian republics started forming, the Church lost all political autonomy for several centuries. Finally, starting with the Council of Trent, things slowly started to improve for the next 300 years, until, finally, the settlement with the unified Italy, and Vatican I.