As you know, SgL, I've been following CP for a very long time. I'm trying to remember when I first started reading it, and it was probably the middle of Volume I? Sometime in 2008?
I've always thought that the way it's marketed (as basically a story hitting the "pleasure slave" kink which is/has been quite popular as you say, MCAH) does it a disservice in terms of the massive complexity of the political plot and the exquisite characterisation and writing. I suspect it started as a kink story that at some point (as many such stories do) got legs and took off running.
Would it have done as well if it was marketed as a courtly intrigue political fantasy, which is really a more accurate genre tag? I'm not sure. I think that excellent writing will always have an audience, but it is also true that Livejournal has always had a strong network of people who like to read M/M fic that hits kinks like this one does. So although I don't think the "Damen is captured and sold as a pleasure slave to a rival prince" synopsis really does the story justice, it's probably been more successful as a "come for the kink, stay for the plot" story that it would have if it were marketed from the outset as a political fantasy with M/M elements.
Which is an interesting lesson to reflect on. I've tried to use some of the learnings from observing Captive Prince in my own marketing, but really I think the lesson is, "write really, really well," and I'm still working on that.