I agree with Alex (see immediately below) that adverse selection need not undo genetic insurance of some kind.
He doesn’t mention abortion, but I view genetic insurance as a possible substitute for abortion. Say you are a young Catholic couple, and you know that you would not abort a Down’s child, even if you detected the abnormality before birth. You also would know that caring for such a child would involve a greater than average financial burden. Might you not buy insurance against this contingency? (Of course many couples simply abort.) Furthermore, couples might buy the insurance when they marry, or at least before they conceive, it would not be hard to make “not being pregnant” as a prerequisite for buying the insurance, if secret genetic tests on the embryo were a huge problem.
The Downs example raises the question of why such insurance does not exist today. More generally, Robert Shiller raises the question of why we do not have more insurance markets than we observe. I don’t think there is a single correct answer. Sometimes I think people simply do not want to face the possibility of encountering certain kinds of difficult events, and buying insurance, in their eyes, admits that possibility into their lives. This obstacle, to me, appears contingent rather than necessary, so I can imagine greater scope for insurance markets in the future. Many financial markets are in any case of recent origin, so why should the growth of markets stop at our current selection?