The service itself would have some value because knowing you can call your insurance provider after an accident and having them deal with everything would really help to reduce the stress of the incident.
My hunch is the insurance companies are a bunch of babies that would rather whine than solve problems. My sister got in an accident in AB last year and it took her insurance company forever to have her vehicle re-towed from a small garage in a little town to Edmonton. IIRC it took more than 6 weeks for her to deal with insurance.
Contrast that with SK where between the city police and SGI you don't have to do anything. They just deal with it and the rates we pay are probably the best in the country. It's ~1500 CAD per year for insurance and as long as you have a decent driving record you don't get penalized for getting in an accident. You can even cause an accident and pay $0 if you don't make a claim on your own vehicle. Plus they typically get everything dealt with very quickly.
If the police are calling corrupt tow truck companies that's it's own problem. That kind of corruption shouldn't be tolerated and if the police are calling a tow truck for you after an accident it should be a regulated process.