Maybe we should have two separate kinds of health insurance?
One for true emergencies (like car accidents), and rare life threatening diseases (like cancer before 60).
Another for routine things, but as others have said, routine things shouldn't be so expensive.
I like the idea of structuring it like a term life insurance policy. If you die, you get money, and in some policies you even get some percentage before you die to have fun.
So, if you get cancer or whatever, perhaps you'd have a pool of funds available to you to deal with the disease, and you can use that money how you want, and perhaps even keep the remainder (or a portion of it) to incentivize keeping cost down.
Also, it would make sense for the pool of funds available to someone to be based on remaining years. If you get cancer when you 20 it makes sense to spend a million dollars trying to cure that. If you're 90, maybe it makes sense to treat it but not as aggressively or in as costly of ways.
From the perspective of building a society that you would be willing to be in, assuming you were randomly born into that society without knowing to what parents, I still think many people would agree they'd rather spend heavily on younger people than older.