Why have some Swiss insurance companies decided not to register?
Simply, because if they did, the U.S. rules would totally govern its business. Consequently, U.S. law, not Swiss law, would govern each and every contract. That means that you would lose the privacy, and perhaps the lawsuit protection etc. that you enjoy under Swiss laws. It is legal for you to contact a Swiss insurance company and to purchase an annuity, but it is illegal for an unregistered Swiss company to advertise in the U.S.