This thread reminds me of an interesting thought I had earlier:

How does Sin exist? For every summoning, be it for an Aeon or for Dream Zanarkand, the summoning is a continuous process. Yu Yevon continually channels the summoning for Dream Zanarkand, and, since we've never seen a summoner take action while an Aeon has been summoned, the process is likely similar for Aeons. So how does the Final Aeon work? The summoner for the Final Aeon dies immediately, yet the Aeon itself continues to exist indefinitely, long enough for Yu Yevon to possess and corrupt it, and then as Sin until it is next defeated. How can it continue without a summoner? If Yu Yevon takes over and controls the summoning, instead of merely possessing the Aeon itself, how does he handle two Aeons at once? If he can handle multiple Aeons, why does he wait for Sin to be destroyed before taking control of the Final Aeon?

Assuming Aeons can survive when their summoner is gone, why does Dream Zanarkand vanish when its summoner is destroyed?

As a side note, why didn't the team simply destroy Jecht's fayth when in Zanarkand, instantly destroying Sin and making Yu-Yevon vulnerable?