Chance,

You make a really good case for Mystery, Babylon being destroyed before the ten kings give their power, strength, and kingdom to the beast, for their one hour with him:

Revelation 17:12 And the ten horns which thou sawest are ten kings, which have received no kingdom as yet; but receive power as kings one hour with the beast.

  13 These have one mind, and shall give their power and strength unto the beast.

  16 And 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.

Because Mystery, Babylon had previously been reigning over the other kings of the earth:

Revelation 17:18 And the woman which thou sawest is that great city, which reigneth over the kings of the earth.

But with Mystery, Babylon taken out of the way, those other kings of the earth will be out from under her reign and sorceries.

That will allow for the beast to have worldwide influence, then power, and then worship.

And it will finally allow for those other kings to be deceived by miracles, to join in the Armageddon campaign against Israel and Jerusalem:

Revelation 16:13 And I saw three unclean spirits like frogs come out of the mouth of the dragon, and out of the mouth of the beast, and out of the mouth of the false prophet.

  14 For they are the spirits of devils, working miracles, which go forth unto the kings of the earth and of the whole world, to gather them to the battle of that great day of God Almighty.

  16 And he gathered them together into a place called in the Hebrew tongue Armageddon.

It also may seem that until she is destroyed, she is like a bully, holding down and suppressing the beast and the ten kings:

Revelation 17:3 So he carried me away in the spirit into the wilderness: and I saw a woman sit upon a scarlet coloured beast, full of names of blasphemy, having seven heads and ten horns.

Apparently, she has so much power and influence, that she holds down the beast and ten kings, like a big bully, sitting upon a smaller, weaker kid.

Until the bully is taken out of the way.

.