I think the problem is in terminology.  Health insurance isn't insurance the way car or home insurance is.  Car and homeowners insurance are there to get your property back to working or livable order.  

Health insurance is more of a cost sharing thing to spread the costs of basic maintenance  and repairs to everybody.  Calling it insurance unfortunately makes people think of car insurance, which it isn't.  Health insurance is more like us all pooling our resources to share the cost of going to the mechanic for both basic maintenance, and repairs to a car.  Yes, I know the analogy isn't perfect, but it is better than any other I have seen.