I spent 6 years in police aviation, and when there was only one chopper airborne to cover Sydney metro area and more, it was mostly to reduce response times. Night patrols were generally pleasant, and the deterrence factor worked many times when we followed a pair of cars into a known dumping area, waited a minute, then lit up the thieves about to strip and torch the stolen car.
Also prevented (or delayed) some pregnancies, when the suspicious cars headed for the dark areas contained people wanting privacy. They didn't get any, so to speak.