Yeah, that's the problem with the Japanese police, but on the other hand that same Japan still respects parenthood more than lots of other countries, so I imagine the son being the prime suspect of murdering the mother isn't as "natural" as it might be elsewhere. But running certainly made sure he won't have any say in the matter.

I'm still not sure if this is better or worse for Satoru's own investigation. On one hand with this he's forcing the murderer to pull off more tricks, thus exposing himself more, yet on the other hand his ability to do any research is limited since he's a wanted man who needs to avoid the public. Not to mention he personally still doesn't know what we, the audience, know. At the very least, assuming he doesn't jump very soon, he will learn that the murderer could also track down his visit to Airi's house. So, he can deduce the murderer has some kind of a connection to the pizza joint.