Neither the city of Rome nor the Papal system are the mother of harlots and abominations of the earth. Both are more recipient than the originator. Mystery Babylon will be literal Babylon in Iraq rebuilt. Babylon has been the center of humanism since its creation by Nimrod.
Jeremiah 50:8 KJV
Remove out of the midst of Babylon, and go forth out of the land of the Chaldeans, and be as the he goats before the flocks.
Jeremiah 51:6 KJV
Flee out of the midst of Babylon, and deliver every man his soul: be not cut off in her iniquity; for this is the time of the Lord's vengeance; he will render unto her a recompence.
Revelation 18:4 KJV
And I heard another voice from heaven, saying, Come out of her, my people, that ye be not partakers of her sins, and that ye receive not of her plagues.
Jeremiah 50:15 KJV
Shout against her round about: she hath given her hand: her foundations are fallen, her walls are thrown down: for it is the vengeance of the Lord : take vengeance upon her; as she hath done, do unto her.
Revelation 18:6 KJV
Reward her even as she rewarded you, and double unto her double according to her works: in the cup which she hath filled fill to her double.
Jeremiah 50:39-40 KJV
Therefore the wild beasts of the desert with the wild beasts of the islands shall dwell there, and the owls shall dwell therein: and it shall be no more inhabited for ever; neither shall it be dwelt in from generation to generation.  As God overthrew Sodom and Gomorrah and the neighbour cities thereof, saith the Lord ; so shall no man abide there, neither shall any son of man dwell therein.
Jeremiah 51:29 KJV
And the land shall tremble and sorrow: for every purpose of the Lord shall be performed against Babylon, to make the land of Babylon a desolation without an inhabitant.
Jeremiah 51:37 KJV
And Babylon shall become heaps, a dwellingplace for dragons, an astonishment, and an hissing, without an inhabitant.
Revelation 18:22-23 KJV
And the voice of harpers, and musicians, and of pipers, and trumpeters, shall be heard no more at all in thee; and no craftsman, of whatsoever craft he be, shall be found any more in thee; and the sound of a millstone shall be heard no more at all in thee;  And the light of a candle shall shine no more at all in thee; and the voice of the bridegroom and of the bride shall be heard no more at all in thee: for thy merchants were the great men of the earth; for by thy sorceries were all nations deceived.
Jeremiah 51:7 KJV
Babylon hath been a golden cup in the Lord's hand, that made all the earth drunken: the nations have drunken of her wine; therefore the nations are mad.
Revelation 17:1-2,4 KJV
And there came one of the seven angels which had the seven vials, and talked with me, saying unto me, Come hither; I will shew unto thee the judgment of the great whore that sitteth upon many waters:  With whom the kings of the earth have committed fornication, and the inhabitants of the earth have been made drunk with the wine of her fornication.  And the woman was arrayed in purple and scarlet colour, and decked with gold and precious stones and pearls, having a golden cup in her hand full of abominations and filthiness of her fornication:
Jeremiah 51:13 KJV
O thou that dwellest upon many waters, abundant in treasures, thine end is come, and the measure of thy covetousness.
Revelation 17:1 KJV
And there came one of the seven angels which had the seven vials, and talked with me, saying unto me, Come hither; I will shew unto thee the judgment of the great whore that sitteth upon many waters:
Revelation 18:16-19 KJV
And saying, Alas, alas, that great city, that was clothed in fine linen, and purple, and scarlet, and decked with gold, and precious stones, and pearls!  For in one hour so great riches is come to nought. And every shipmaster, and all the company in ships, and sailors, and as many as trade by sea, stood afar off,  And cried when they saw the smoke of her burning, saying, What city is like unto this great city!  And they cast dust on their heads, and cried, weeping and wailing, saying, Alas, alas, that great city, wherein were made rich all that had ships in the sea by reason of her costliness! for in one hour is she made desolate.
Jeremiah 51:49 KJV
As Babylon hath caused the slain of Israel to fall, so at Babylon shall fall the slain of all the earth.
Revelation 18:24 KJV
And in her was found the blood of prophets, and of saints, and of all that were slain upon the earth.
Jeremiah 51:58 KJV
Thus saith the Lord of hosts; The broad walls of Babylon shall be utterly broken, and her high gates shall be burned with fire; and the people shall labour in vain, and the folk in the fire, and they shall be weary.
Revelation 18:8 KJV
Therefore shall her plagues come in one day, death, and mourning, and famine; and she shall be utterly burned with fire: for strong is the Lord God who judgeth her.
Jeremiah 51:62-64 KJV
Then shalt thou say, O Lord, thou hast spoken against this place, to cut it off, that none shall remain in it, neither man nor beast, but that it shall be desolate for ever.  And it shall be, when thou hast made an end of reading this book, that thou shalt bind a stone to it, and cast it into the midst of Euphrates:  And thou shalt say, Thus shall Babylon sink, and shall not rise from the evil that I will bring upon her: and they shall be weary. Thus far are the words of Jeremiah.
Revelation 18:21 KJV
And a mighty angel took up a stone like a great millstone, and cast it into the sea, saying, Thus with violence shall that great city Babylon be thrown down, and shall be found no more at all.
It's in the wilderness (Rev. 17:3) or desert. Rome isn't, but Babylon is. Babylon of Revelation 17-18 matches the description of the land of the Chaldeans (not the Romans) in Jeremiah 50-51. Her name is not Mystery Babylon, as if this was a mysterious and different form of Babylon. Her name in the KJV is, "MYSTERY, BABYLON THE GREAT." There's a comma there showing these are two names. The Bible said it's "Babylon the Great." So it's Babylon the Great. The seven heads as seven mountains requires wisdom to understand (Revelation 17:9). But it required no wisdom at all to know the famous seven hilled city was Rome, so that isn't what's going on here. The seven mountains (not "hills," a mountain is a very large hill) must be symbolic then for seven kingdoms (as a mountain is a kingdom according to Daniel 2:35, 44). This goes along with the seven kings in the next verse. Revelation 17-18 is prophetic and deals with events in the Tribulation, to come "hereafter" (4:1). It doesn't deal with the Church Age. So it can't be describing the Roman Catholic persecutions in the Dark Ages. The Whore is the mother of harlots and abominations. That fits Babylon, which originated idolatry; rather than Rome, which is just a daughter or product of Babylon's idolatry.