But if your auto insurance policy also covered a catastrophic engine failure, the company would probably insist on covering some routine maintenance items like oil changes. This is probably a better parallel to health insurance. Yes -- your health insurance should cover only major costs and catastrophic events. But the insurance company would really want to cover itself and stay on top of its customers by covering "routine maintenance" -- so big problems are discovered and addressed early on.
Not so with health; as lifespans increase, the probability of major health care services being individually required basically nears 100%. Obviously, this outcome cannot be insured, which is why nationalized health works from a maintenance perspective. That is, you may not get great care, but you also won't be left to die on the side of the road.
Add to that mix the ill, poor & indigent, and you have a baseline demand for basic healthcare among those who cannot afford it. Since society will not turn them away, the middle-class ends up paying for them anyway in the form of greatly increased health 'insurance' premiums/deductibles for themselves.
The solution, of course, which may eventually be reached, is to have two tiered approach: (a) basic services provided for the ill, poor & old, and (b) 'insurance' for the great center of healthy, working, self-sufficient, young/middle-aged people. In this way, health insurance would actually work, since risk could reasonably be measured and assigned. But once people move past 55+, it longer is really insurance; rather, it's practically inevitable that a major health care event will occur.