An insurance company is a bureaucracy. It is not capable of diagnosing patients. All it knows is paperwork. But if doctors and therapists all use a common diagnostic standard, then the insurance company can put every customer in a box.

Then when your doctor diagnoses you with X and prescribes treatment Y, the insurance company can look up X and Y and tell that your policy doesn't cover it. Another job well done.

Without the DSM, there would be no way to know what your policy does not cover.