This is because insurance companies pay in base on what you did or how long you did it. You itemize each visit like a tax return that later gets reviewed. Then someone reads the return and thinks if it makes any sense.
After that, they pay back the doctor, but according to the plan, they also have to charge the patient the copay.
That said, a doctors office that is only cash will get very little patients. Because people that are employed will not go to a cash-only doctor's office.