"...Alternatively it suggests the device could have been switched off/disconnected from the network to hide your presence - making you really a suspect of interest if your name comes into the investigation for some reason..."

That's really interesting. If I'm understanding you correctly, people who routinely switch off their location services, could potentially end up as suspects in crimes if they, for instance, live in the apartment across the hall from the victim or something.

So keeping location services on let's the police keep tabs on you, potentially making you a suspect in some crime in the future. Alternatively, turning it off potentially turns you into a suspect of interest in some potential crime in the future.