Ack8236 I think a disservice is done by the marketing folks that work for insurance companies. Many make it about price, when it should be about coverage. No one has a major loss and goes, "Thank God for cheap insurance!". They actually say something like "I hope this is covered."
I also do not care for the commercials that advertise this false sense of expectations. Like a good neighbor, State Farm don't care. You are not in Good hands with Allstate, and Nationwide is not on your side. An insurance policy is a contract.
Of course insurance companies are in business to make money. They need to remain solvent to pay losses on the policies they issue. The State Bureau of insurance makes sure they have the financial reserves to meet their obligations.
You are correct about self insuring not being an option for most people. It makes no sense to self insure when you can get coverage for pennies on the dollar. Like it or not insurance is a tool that makes the world go round.