This article from The Economist looks at the same issue. At the end, almost as a throwaway, it comments that this issue may become a compelling argument for national health. The whole point of insurance is to pool risk, and risk equals uncertainty. As genetic screening becomes ever more accurate, so the uncertainty is decreased, and both individuals and their insurers can more accurately predict the cost of future healthcare.
This leads inevitably to a genetic underclass situation where people who show a long term predisposition to expensive diseases will be unable to insure against them or to pay for treatment if the disease develops.
Now consider the motivation of a couple planning a child. Their child might turn out to have some nasty genetics, but you never know.
In theory at this point they could buy life-time medical insurance for the unconceived child, but in practice this would be very expensive. They could pay in instalments, but it would be hard for insurers to enforce the contract against those who subsequently have genetic tests, find themselves in the clear, and decide to let the cover lapse. They would still owe money, but getting it out of them would be difficult. Also this scheme predicates an individuals entire health care for life on what their parents were willing and able to pay before they were born!
So for our putative prospective parents the idea of state health care for their child looks very attractive. The risk is shared, as in conventional insurance, but without the adverse selection problem because its compulsory.
In fact this problem is already with us in a small scale. Ask anyone with epilepsy about health insurance. You might be able to get it, but it will exclude anything related to the epilepsy. So every few months you wake up in Casualty owing them $5,000, and there is nothing you can do to stop this (short of permanently wearing a tee shirt telling people not to call an ambulance if you have a fit).
Genetic tests will bring this problem to a significant minority of the population, at which point they become a constituency that politicians will seek to please. Also there are those people planning families. I'd guess most people expect to have either children or grandchildren at some point in the future. If we start to see significant numbers of babies declared uninsureable for things that are likely to first beggar them and then kill them then pressure for national health systems will grow.
Of course I live in the UK, where we already enjoy the somewhat dubious benefits of the National Health Service (NHS). Its not exactly the best care money can buy, but it sure beats being uninsured.
You are lost in a twisty maze of little standards, all different.