I agree with your points, but the result will probably just be higher rates, not failure. You can see it start to happen already with the early implementation of the ACA. However, that that isn't what I was talking about, and it doesn't support the parents claim that, "they [insurance companies] can have access to a good set of indicators to remove people with high incidence of diabete, kidney failure or cancer, they will use it."
My point was, no, insurance companies can't use the data, even if they had access to the it, which they won't.
I was wittering on about this earlier today: https://news.ycombinator.com/item?id=6807778 and other comments in that older story - but my brief summary is: if you know your genetic data, you can then make insurance policy choices based upon it without telling the insurers. But when enough people do this collectively, the insurance market will (possibly) fail or be forced split offerings into various levels of cover. Customers then self-select and the end result is the same as if the insurers knew the data in the first place.
At this point do you really need the genetic data to get the same effect? I throw out my back, I upgrade my insurance, then I get the surgery. The doctor says I have 90% blockage in my arteries,I upgrade insurance, then I get the bypass. It seems like genetic data will have less influence than people making changes based on empirical observations of their health.
I don't know specifics about the USA, but certainly in the UK, private healthcare insurance works like most other forms of insurance, i.e. Pre-existing conditions or other relevant information is either not covered or must be declared and will be used to adjust premiums.
No car breakdown insurance lets you take out a policy to cover the vehicle after it has already broken down...
1) More high risk customers buying the insurance concentrates the 'pool' of insured risks...
2) ...leading to more payouts
3) ...leading to higher insurance
4) ...leading to those without the risks opting to take cheaper, lower level coverage
5) ...leading to more concentrated risk in the pool of insured people in the good coverage
6) ...and back to step 2. The insurance fails, or becomes too high a cost to be worthwhile for anyone.