I imagine it doesn't always work, but it was a last resort for me after DH's accident last year. Insurance was refusing to replace seats and insisted they were safe to use. I did ask for a letter from them stating that and also that they would assume any liability if the seats failed in a future crash. They did agree to replace my seats.
It was a last resort after I had exhausted all other avenues, and I don't know that it would always work, but it was all I had left. I also had to argue that they wanted to put replacement value as the cheapest price they could find, and I had to point out what the true replacement value in-store was so I could get new seats ASAP without having to wait for shipping. They did agree to the in-store price when I pointed that out.
Good luck OP!