Wasn't it stated that Xemnas simply built the Chamber of Repose as a mirror to the Chamber of Waking? I believe Zexion called it his "usual spot," implying that he goes there regularly to talk with Aqua's armor (as we see him do in a final mix cutscene), which he presumably moved back there so as to have some level of privacy when discussing things with her/it. Only realistic reason I could see for him wanting to do that though is just so that no one gets a glimpse into his true motivations and/or character by eavesdropping. It's VERY important that maintains that demeanor of cold, absolute competence whenever around the other members, so as to both intimidate them, and also make it seem as if he always has things under control (or at the very least isn't phased when issues arise). In fact, one of the only more casual conversations I can remember Xemnas having with any other Organization memeber, would be his 1 on 1 talk with Roxas at the dark margin. That interaction seemed noticibly less rigid and professional than any later talks they have, and Xemnas seems more interested in hearing Roxas' thoughts on Sora than giving any orders or opinions himself (which is interesting, as one could look at this as Xemnas talking to one of his subordinates on a more equal level, but the conversation is relatively short, so we don't get to see where it might have gone). In any case, Xemnas had several personal agenda's he didn't want anyone knowing about (like his memories of Terra and Xehanort and how that motivated him to reunite with Ven, the plan with the thirteen Seekers, the whole hang up over Subject X, etc.), so it makes logical sense for him to create a private room where he can discuss or go over these things with himself. Someone will have to remind me if this isn't the case, but I can't remember much more being said about the Chamber Repose itself that was still left unanswered (aside from Aqua's armor and Keyblade, which by all means should have been addressed in Kh3).