Here's a hypothetical example: Say there's a horrific genetic condition (let's call it 'The Lurgy') that would involve lots of expensive treatment if you developed it. Now, a cheap genetic test kit comes along that can give an accurate prediction of whether or not you are likely to eventually suffer from the lurgy. What happens?
The first effect is that more people test themselves, and go out to buy quality healthcare plans if they see that they are going to get the lurgy. These people might not have otherwise bought the insurance. Result: the insurers suddenly get a much higher % of lurgy sufferers. Their costs rise, and this pushes the insurance price up. This exacerbates the problem: Non-lurgy people are less likely to buy the insurance. Worst case, the cost of insurance comes close to the general cost of treatment, meaning that the insurance is useless.
BUT: The obvious counter to this is that the insurance companies can adjust their range. They can split their insurance offerings up into two products: One that covers the lurgy, and one that doesn't. People are free to buy either. Naturally, the lurgy-inclusive policy is much more expensive. Suddenly the risk is back on to the consumers. They don't have to declare their genetic tests, and the insurers can't force them. But now they can't afford not to take the genetic test and buy the appropriate insurance (and in so doing, effectively 'declare' their genetic test results - after all, you'd buy the cheaper insurance if you could)
So the endgame is that everyone suffers. You can imagine a world where there are genetic tests for all kinds of disorders and combinations of insurance coverage that cater for all. But now the insurance pools are smaller, the uncertainty of costs is reduced, and so the insurance costs come closer to the expected costs of treatment. i.e. insurance costs are high, the insurers still profit, and the benefit to the consumer is vastly reduced.