What about treatment for severe conditions such as cancer or chronic conditions such as life-long disabilities where the expense is significant to the point that it may well be crippling for an individual but is rare enough that it's only a moderate cost spread across a society?

These are the cases where insurance is a perfect fit. The issue with letting it be market-based insurance is that (as you say) it allows insurance providers to take a fat cut. The obvious solution is to regulate insurance costs. At which point you might as well state fund it. Which leads us to the system we have in most of Europe.

As these system seem to work quite well, why do you think a market-based approach would be better?