Even if all the insurance plans and schemes were just trying to "break even", premiums must vary with the price of health care.

If demand for health care goes up, and the supply of qualified caregivers and facilities is fairly constant*, that price will undoubtedly go up.

Thus the price of insurance premiums would go up, unless the premiums are severly subsidized, or the amount (or quality) of  healthcare is rationed.

There may be a flaw in this analysis, but I can't think what it is.
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*  Yes, more caregivers could be trained, and more facilities could be built, but where would the money for that come from?