I've proposed several alternatives to the adverse selection explanation for missing insurance markets. Here's another, with a somewhat Hansonian flavor: In part, people buy insurance so they don't "look stupid" when something bad happens to them.
If you get in an auto accident and you don't have insurance, then most middle-class Americans will consider you an idiot. But for some reason, they don't consider you an idiot if you fail to buy long-term care insurance and suddenly need it - even though it could be argued that long-term care is a smarter buy than a lot of auto insurance.
The result is multiple equilibria. If most people buy insurance and you don't and something bad happens to you, you get a double whammy - the direct loss plus the idiot's stigma. If most people don't buy insurance and you don't and something bad happens to you, you are only out the money. If most people buy it, you want it too; if most people don't, you probably don't want it either.
By way of analogy, consider these two scenarios:
1. You lose $1000 in some unforeseen way.
2. You lose $1000 in a way your spouse specifically warned you might happen.
It seems to me that #2 is MUCH worse for most people than #1. $1000 is no big deal; but $1000 plus the scorn of your spouse is a very big deal. Now think how much worse it would be if everyone took your spouse's side against you. Ouch.