It IS possible to have an ethical for profit health insurance company, but difficult.

The ceo/board has an obligation to maximise profit for shareholders, there is such a thing as a “minority shareholder lawsuit” so even if you control 90% of the shares, if 10% of the shareholders decide that you arent acting to make them as much money as possible they can still sue. There are ways around this like having the companies mission statement be “95% of premiums will be paid out as customer claims.” Or similar. Making their money by having a larger market share or by vertical integration.

It could be done ethically, but it wont be.