Rome was already viewed as a "Greater Babylon" for having conquered Judea just as Babylon had done centuries earlier.
That doesn’t prove their views were right. Nothing stops people from misinterpreting Bible prophecy or having erroneous conclusions about what the Bible means.
In Revelation 16:19 she is described as a city of the nations and not identified as a nation or an empire. In Revelation 17:5 she is described as the mother of disgusting things of earth. That isn’t secular. In the Hebrew bible it identifies idols. So the mother would not be a world government or empire—which also has a different destruction in Revelation. Throughout human history humanity till this day including nations practice heathenism, some emperors like in Japan also idolized. The Roman empire doesn’t fit cinderella’s shoe. Neither did Rome have the same ending as BTG pictured in Rev.
Given the book of Revelation is from God, it is non sequitur that the BTG was Rome because Rome was not destroyed like BTG, Constantine and the Roman Catholic Church till this day, no Roman Empire today, and still waiting for BTG whatever her identity is to suffer the fate told in Revelation. It makes a lot of sense to me that idolatrous lies and its mother identifies the religious entities of the world.