GentlyFeral,
I was not trying to be too serious here. But if you're having trouble with the analogy then that's part of the point.
Bible beasts admittedly represent nations, and this particular beast is supposed to the the "nation of nations" or the United Nations. But if all religion is a whore riding on the nations then there must be a "services rendered" by religion, and a "payment for the services" that these nations have "enjoyed" (which somehow they will tire of). The most well-known relationship between religion and the state is the tax break for non-profit status. It involves a services rendered (charity) and a payment (effective tax refund).
You're right, that if we got very serious about this then we might look for only clandestine or unsavory services rendered and the payment being some sharing of power with religion (non-separation of church and state) which is a more likely thing that nations would tire of.
I don't particularly care what Revelation means, but if I were to guess at the original author's intent, I would think it was pointing to the idea that God's judgment had just been poured out upon Jerusalem, which had often been called a bloodguilty "harlot" in the past. It had spilled the blood of the prophets before, and had recently played with fire in getting Rome to do the dirty work with the execution of Jesus. So in spite of Jerusalem's taxes, and friendly ties with the Herod's etc., Rome tires of her games by 70AD and continues bringing God's judgement upon Judea well into the 130's AD. But a New Jerusalem, a new Bride, a new Nation, will remain without spot from the world of Rome, etc. etc.
I'm sure there are other possible explanations that have proved more appealing throughout history, but for me, this one seems to best fit the author's original clues.
Gamaliel