In my opinion, Co-Operative groups can compete with Private insurers. As in the not to distant past it was not uncommon for co-operatives to maintain insurance risks as well as and in many cases better than private insurance companies. In fact in the United States fire, health and life insurance co-operatives were set up and were so successful that they were the inspiration for private insurance corporations to form and accept the risks.
Co-ops are run as a non-profit insurance alternative, and are owned by the consumers who use them. Unlike private insurance companies, they would tend to offer better services at lower prices. All of it depends on the number of users. The more users, the lower the prices and better the services.