Nor is western civilization conceivable without the existence of the Roman church. From the very beginning of Christianity, the Roman empire made physically possible the rapid propagation of the Christian message. This was realized and admitted by some early Christians, who themselves saw, in the peace and the security of the Empire, an act of divine providence. The empire provided the incentive and the opportunity for them to organize and centralize the new faith.
As early as the second century AD, the bishops of Rome were being recognized as the successors to Saint Peter and [as] the heirs of his apostolic primacy. But, in addition to this, the very fact that the Roman church was situated in the capital of the empire gave it a universal character and an authority which the other great Christian communities could not hope to attain. The road was opened which, eventually, led to the papacy.
From: Rome in the Augustan Age by Henry Thompson Rowell; The Centers of Civilization Series, Volume 5 (Norman: University of Oklahoma Press, 1962), pp. 230-231.