Either the murderer was looking for something small (what can be hidden in torn paper?), and it can be anything, I mean, a gem, a ring, a photo, a microphoto... or, he simply didn't care whether he left traces or not, because he planned to set the house on fire? Something prevented him from doing it, either own wound, or difficulty escaping in such a case, or maybe he realized he won't run too far away before the police would come, but makes me wonder if he came with a more thought-out plan. One reason he left so many traces is because his ultimate idea was different, he didn't think there'd be any traces left.
I think that either his wound or something else precluded it. One wonders. Maybe he found what he came for.
ETA: so let us imagine...if it is something personal. I am not sure but imagine. He comes to retrieve something that may threaten him (I can only guess, how). He wants to slide in, but ends up waking people up and killing them. After that, he goes through documents. Then, through torn paper. Then, he dumps it into bathroom...this something is either small but heavy, so he'll hear, or it looks different. Did they still use Polaroid in Japan in 2001? Some of the family photos look as if made by the Polaroid. A Polaroid photo stands out. Anyhow - something tiny but incriminating for the perp.
I think that he found it. And left the moment he did. Had he not, he'd set it all on fire.
What do you make out of different age brackets provided by the police,
@FacelessPodcast?