My theory is Kellhus built the 2nd palace for the same reason the non-men built the threshold to hide from the gaze of gods. Esme then tells Kel about it, who seems to have exclusive use of it, only Esme, Kellhus and kel know about it
The thing has no practical use for Kellhus he doesn't need to run about the palace and spy on what folk are saying, he can see through fire, can see their thoughts etc. Ostensibly though it is a good cover story.
Better than Kellhus going, yeah i'm building a maze type thing so in a few years when i'm with the great ordeal you'll tell our youngest about it who will use it to spy on a god sent assassin unseen and then disrupt his plan to kill me when i return from Dagliash to spring the trap, and finally show the gods they can be blind.