The intersection of chronic, treatable conditions and low probability, high cost events is not empty. You could find a condition with any combination of being

The intersection of chronic, treatable conditions and low probability, high cost events is not empty. You could find a condition with any combination of being chronic, acute, low probability, high probability, low cost, or high cost. What you're really looking for is getting insurance out of covering expected medical expenses, but the problem is that doctors and hospital charge higher prices to the uninsured. I had a medical bill once that was denied by insurance, and the hospital wanted something like $12,000. Later we got the insurance to pay, and the hospital only charged them $2,000 or so. A related problem is that the tax code favors insurance companies by providing a tax break to employers, which is why most Americans get insurance through their employer.