This is one case where the libertarian argument that governments are fundamentally coercive works against you. Insurance companies can't take such broad actions to protect health as government can -- things like taxes on products with negative health externalities, regulations ensuring workplace safety, etc.
The argument here was about incentives -- i.e. the practical component of how our laws get updated, not about the theoretical component. Your original argument was that private companies are incentivized to pursue safety, and my counterargument is that incentivized private companies do not nearly as much power to effectively pursue safety as incentivized governments do.
