Insurance company profits are already capped by law. I don’t think your ideal insurance company would be much better for the customer than the already-available options are.

The companies must spend at least 80 cents of every dollar they collect in premiums from small businesses and individuals on health care, and 85 cents per dollar for large employers. The remaining 15 to 20 percent is all they are allowed under the Affordable Care Act to spend on administrative costs like overhead and marketing and to keep as profit. Any additional revenues are to be returned to consumers in the form of rebates.

Note that the remaining 15 to 20 percent has to cover all the costs of actually running the company. It isn’t just profit.

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Insurance companies do have to compete with each other on price. Employers who provide insurance want the cheapest insurance that their employees will tolerate. Healthy people want the cheapest insurance that they expect to protect them from sudden, catastrophic expenses. If your business plan is to spend more money than the existing insurance companies do, and your target market is people unhappy with their current insurance companies (these people are probably have expensive problems) then you’re not going to do too well…