If insurance companies operated as non-profs, do you think the cost of insurance would go up, or down?

I'm not sure on the accuracy of the claim, but someone on GAG said that average profit margins of insurance companies are 2-5%. If they lost that profit margin, ideally, the rates would decrease by that same amount. However, if they covered all requests as a result, the insurance rates would increase to cover the increased costs of providing payment for that treatment.

So the real question is, would the additional coverage outweigh the eliminated profit margins? I'm not an expert in this field, so your guess is as good as mine.

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Let's also say the CEO makes $0 per year as well. This would add millions of dollars to a multi billion dollar budget.
If insurance companies operated as non-profs, do you think the cost of insurance would go up, or down?
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