Things I don't understand: health insurance

This will not be an intelligent post.  I do not have intelligent things to say about health insurance..  I do not understand health insurance: what is good about it, what is bad, and the impact of various policies.  I am also unable to make sense of what the internet tells me about health insurance.

Health insurance costs money, and what it gives in return is money.  But if that were all, it seems like you can't really win against an insurance company that is still in business.  Why is insurance ever worth it?

Most insurance is about reduction of risk.  If you don't have homeowner's insurance, a house flood could financially ruin you.  But if the cost of home repairs were spread out over all possible worlds, it might be easier to handle, even if there is some overhead going to an insurance company.

Of course, there's always this problem where different people have different levels of risk.  Either there ends up being price discrimination, or insurance becomes too expensive for people with low risk, or insurers refuse to sell to people with high risk.  I think Obamacare is meant to solve this problem by encouraging everyone to buy healthcare regardless of their level of risk, and by putting restrictions on price discrimination.

Although it also seems that risk reduction is not the only function of health insurance.  Why does health insurance pay for regular check-ups, and why is it so expensive to pay for health care independently?

Maybe it's a little like restaurants.  In theory, restaurants should be cheaper than cooking at home, because they benefit from economies of scale.  In practice, restaurants are often more expensive because they offer service, space, and food quality.  The economy of scale, the service, the space, and the food quality often come in the same package because it's efficient to do it that way.  Perhaps the same is true of health insurance: risk reduction and regular check-ups come in the same package because it's efficient to do it that way.  I'm not sure why though.

One idea is that preventative screenings are cost-efficient, but people irrationally avoid them because they cost money now.  By reducing the marginal cost of preventative screenings, health insurers actually make health care cheaper by bypassing a psychological obstacle.

Another idea is that health insurers are able to allocate people to doctors or health care providers more efficiently than independent buyers of health care.  Or they reduce administration costs.

One last idea is that health insurers create a monopsony, which is like a monopoly except instead of one seller, there is one buyer.  Because there are fewer health insurers than people, they have more power to tell health care providers to lower their prices.  I barely understand how a monopsony works, but it causes prices be lower than the "efficient" market value, whatever that means.  It seems to me that the more of a monopsony there is for health care, the more of a monopoly there is for health insurance, and I don't understand how those things interact.

Many progressives advocate going further than Obamacare, adopting a "single-payer" system.  I don't understand what the impact of this would be.  I guess it would create more of a monopsony?  People on the internet say it will reduce administration costs.

Dear readers, do you understand health insurance, or no?