It seems this would be the same as car insurance also paying for tolls, road maintenance, car maintenance, etc. instead of just covering against person/property injury from vehicle operation.
If health insurance instead is used for typical day-to-day payments for health care coverage, then the costs of that insurance will logically exceed the cost of that care because the insurance company exists to make a profit through offering that service.
Similar to paying the government to do something that would be more efficiently done privately - Maybe the same outcome (if one is fortunate) for far greater cost.
Anecdotally, I used to have a health insurance plan that had a very high deductible and fairly low monthly payments for my wife and myself. It's sole purpose was to hedge the bet that one of us might need ambulance and major medical treatment at an expensive facility (hospital) that might break us financially without that hedge in place.
The Affordable HealthCare Act in the USA ended that arrangement, we now have triple the payment size for a third of the coverage we used to have. To me, that is a clear case of my government getting involved and the results being a net loss.
Edit: Sorry, it did not end that arrangement, it made it far, far more expensive.