My thoughts exactly. In fact I would modify this to:
> the motivation of insurance is to keep the cost of treatment that they cannot avoid liability for less than the income from premiums
Yep - the motivation of health insurance is to keep people out of hospitals and away from healthcare professionals as much as possible.
Sometimes that aligns with keeping people healthy, but other times that aligns with women not getting routine prenatal screening and thus increasing the infant mortality rate.
The motivation of insurance is to keep the cost of treatment less than the income from premiums -- it doesn't have anything to do with how healthy people are.