Based on what the Pres said, the Mysteries act like part-time protectors of the the school. So is it kind of like Guardian Deities of a land? And if it is, do they also require some sacrifice? If all this is the case, then Nene's short life-span is because she is suppose to be the sacrifice for the school mysteries, and the removal of each of the Mysteries is to prevent Nene from being sacrificed.
Yes, this arc does have the sacrifice thing to be No.6's idea but its possible that he's just being the proactive member of the mysteries, which resulted in him taking Aoi. Whether Hanako planned this or everything just coincidentally fell into place, he seems satisfied with the result.
Chapter 68 seems to imply that Hanako was lying to Nene about students not being sacrifice, and it's possible that Tsukasa and Hanako were the latest sacrifice that kept supernaturals at bay until the present.