Not all things the free market produced actually have resulted in better health outcomes than if they had been disallowed (many result in the opposite, in fact) and certainly not better economic outcomes for the people who bought and used them. Regulation, as always, is a balancing act between enabling those who would do good and stymieing those (who with the best of intentions or outright sociopathy) would do harm.
So yes I remain unconvinced. Free market maximalists tend to highlight their favorite part of the story while ignoring history.
Regulation has not always resulted in better health outcomes than if the product had otherwise been regulated either. We don't need to set up this false dichotomy between markets and regulation and then bash markets over the head with the negatives aspects while ignoring negatives outcomes as a result of government action which you seem to be insinuating.
So to remain unconvinced doesn't make sense here. Though I guess I can just say I'm unconvinced of government regulations because why not? Same line of reasoning that you're using here.