You have no evidence for this claim that babylonian religions were practiced in Rome. It was based on a book that was later retracted by the author
http://en.wikipedia.org/wiki/Babylon_Mystery_Religion
The religion of Rome at the time John wrote that was paganism. The paganist religions of the roman empire were later abandoned in favor of Christianity. That conversion of the roman empire to Christianity may be what the destruction of the harlot represents.
"16And the ten horns which thou sawest upon the beast, these shall hate the whore, and shall make her desolate and naked, and shall eat her flesh, and burn her with fire.
17
For God hath put in their hearts to fulfil his will, and to agree, and give their kingdom unto the beast, until the words of God shall be fulfilled. "
A number of Roman Emporers, the kings or horns of 'the beast', eventually turned against against paganism and introduced Christianity to the empire. This was the end of paganism in most of the world which was then replaced by Christianity.