You'd rather have Kanon coming in, taking Battler's place in the closet, and then switching personalities/giving up Kanon's personality as a solution and an acceptable dodge around the red truths (with it all coming undone as soon as Erika opens the door and sees who is inside), than an acceptable and inventive way to exit the room that has many hints laid out all through the chapter?
It's not what I'd rather have, just that it seems to be the case.
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"As the size of an explosion increases, the number of social situations it is incapable of solving approaches zero." -Vaarsuvius, Order of the Stick