It's always difficult to post about health insurance, because to a great degree health insurance has ceased to be "insurance." But, anyway, I still want to think about it as an insurance problem to consider the many reasons why there's a serious market failure problem.
So, continuing where I left off a few days ago. Imagine that we all enter adulthood as identically healthy adults at age 18. We purchase an insurance contract annually, and with a perfectly competitive insurance market the premium is roughly "actuarially fair," that is, roughly equal to the expected loss (probability of illness times cost of illness). In the last thought experiment illness probability (or more generally expected annual health costs) was simply an increasing function of age. That is, your annual premium rises with age.
The problem with this example is that it implicitly assumed total average annual medical costs were independent draws from some distribution which were uncorrelated across time. That is, getting sick this year has no impact on whether (and how) sick you'll get next year. That of course isn't realistic. The big medical costs - and expected future medical costs - arise when you're diagnosed with a chronic condition (AIDS, diabetes, hypertension, muscular/nerve degenerative diseases, etc...) which both require expensive ongoing care and increase the probability of additional conditions/associated costs later in life. As Jim Henley says, this is less about health risks and more about "health certainties" - at least, ex post, after the diagnosis. Ex ante it's about risk of course.*
So, what you'd like to be able to do is, at 18 when you're still young and healthy, buy a lifetime "no fault" health insurance policy. If you develop a chronic condition of some sort, your premium doesn't change, and premiums are just based on the expected loss for the entire risk pool of the insurance company, rather than your own personal expected lifetime medical costs. But, contracts which operate under such a long time horizon are always problematic -- the firm can go bankrupt, etc (something quite possible even for a responsible insurance firm for a variety of reasons). And, if you wake up at age 47 with a chronic condition and a contract with a bankrupt company, you're basically screwed.
Employer/group policies in some sense act this way. With some wrinkles around the edges, you can't be denied coverage for pre-existing conditions, and at least for large employers this works well enough. But, this of course makes insurance dependent on steady employment with a benefit-providing company, which can be problematic especially if you, you know, get seriously sick.
*First to respond to Jim's point about how in my rough word model revenues precisely=insurance payouts, leaving no room for overhead, reasonable rate of return on capital, etc... Just a standard simplification, and doesn't impact the basic analysis in any simple way.
**And, yes, even the "certainties" have an uncertainty associated with them - time of death.