EDIT: Yes, that creates a data point that police could also search for — "give me all the phones in the vicinity that were turned off and then back on surrounding the incident." Okay, how far away? That would be a massively larger search, geographically, wouldn't it? How far before and after is your window for turning off and back on events?
That's still an additional search. It's also probably got a far worse signal:noise ratio than proximity to the incident — assuming the robbers were dumb enough to have their phones on them (and on) in the first place.
But most people don't unless it runs out of battery and rarely when they are at home (people just plug it in when they are home).
Not that this is useful in court but it could point detectives in your direction.
Leaving it at home, without turning it off, leaves no such trace; it's consistent with "this phone's user simply stayed at home today".
"We got 'em!"