Because it was the fourth kingdom to be conquered by God. They believed that God had promised to set up his church on the remains of this fourth kingdom. Christians flocked to Rome and were killed because they sought to convert this final evil kingdom. This is why, even though Babylon was essentially gone by this time, Peter says he is writting from "Babylon" when he is in Rome.
Of course, the RCC believes that the prophesies were fullfilled when the Church took over the Roman Empire. Some NCs believe that the RCC is that fourth empire (and the "whore of Babylon"). But everyone agrees that the empire spoken of is Rome. The early Christians were just trying to be part of the fulfillment of prophesy.
That's all fine and good, but once the church conquered Rome, why wouldn't Peter go back and set the main headquarter up in Isreal. Take the enemy home rather then make home with the enemy.?
Becky