Good catch on Light's ability to access sensitive files on his dad's computer.
Although most home routers typically do not record individual file access on a local network, they do record the connection time, local IP, and the device id of any computer that connects to the network. Also, certain types of computer may enforce access file access logging depending on the operating system and file sharing protocol.
Also, it is reasonable for organizations like the police to use a VPN for sensitive data, which could not be accessed on a home network without authentication.
In the real world, all that L would need to do is to inspect the router logs in all the police households to figure out which computers had access to the network at the same time. That would instantly narrow down his list of suspects. Guess he's not a cybersecurity guy... 😁