Earlier quoted context omitted.
As an aside, this is why buying insurance, despite being a financially bad bet (or the insurers would go out of business), actually is a sensible thing to do from a quality of life perspective.
Insurers are often mutually owned by their customers, so they don't need to profit.
Profit is only one part of the overhead. They also have to pay agents, adjusters, underwriters, managers, office stationary, postage, fraud investigators, lawyers, taxes, interest on bonds etc.
Similar for hospitals etc. Profit, ie cost of equity capital, is usually (but not always) a relatively small part of an organisation's overall cost structure. And the non-profit alternatives typically don't have meaningfully lower costs.