Part of the problem is possibly that in the UK, police & air ambulance a/c are civilian, and have to be operated to Cat A most of the time. That precludes hovering over cliffs etc carrying out winching. Also, the weight penalty from sticking a winch on the side of the aircraft means that you would reduce the endurance or crew in the primary role of policing or ambulancing, unless you buy a great big expensive helicopter, which police forces and charities cant afford.
That is why in the UK the SAR service is provided by the military and coastguard, where there is public funding which allows the right sort of aircraft to be used.
In many European countries, police aircraft are operated under paramilitary rules, and also have different funding arrangements, making operation of specialist rescue aircraft a more viable option.