IMO, Accident Management companies do bear a degree of responsibility for driving up motor insurance costs, but we should remember that it was the habitual foot-dragging and general unwillingness to settle fairly by insurance companies that provided the opportunity for them to operate.
Ideally, insurance companies would act promptly and fairly to ensure injured parties are put back in the position they would have been in had the incident not occurred, and there would then be no market space for accident management companies to operate in.