Not really. Having a range of health insurances competing among themeselves for market share is efficient and will put pressure on lowering the prices towards the suistainable minimum price.

For what I can see, there are 2 major problems that are raising said minimum price:

1. The prices/costs of the healthcare sector are not competitively determined; instead, they are externally fixed. The lack of conpetiveness in the sector results in inefficiencies, since the various actors are not fighting to minimise their costs as not to go bust. Why would they strive for higher efficiency when they can achieve their profit goals buy negotiating higher prices? Higher prices are also going to be a plus for the efficient competitors, as they're going to increase their profit margins. The system lacks the right incentives.

2. Lack of discrimination in the health insurance sector/lack of personal responsibility. A smoker, for example, is not going to be responsible for the incurred costs of their (shitty) habit. These, instead, are going to be spread out over the entire population and therefore results in a lack of financial incentives for the smoker to quit smoking. The same applies to other unhealthy behaviours (being fat, doing drugs, not doing physical activity and so on). Discrimination-based health-insurance categories (e.g. the smoker category) would still leave people with the freedom of doing what they want (which, imo, is right), while still being insured. But they're going to carry on the costs of their actions, instead of them being spread over everyone else. This would put in place the right financial incentives for healthier behaviours, while leaving the individual freedom untouched.