No, you don't get to impose simple answers about a complex topic. Violence is justified when it comes to self defence, which is why we form governments. Public health also extends to stuff like food safety, which can protect people from poisoning in case the producer decides to cut corners.

You do realize goitre and cretinism were a very serious medical condition. It is now almost completely eradicated due to salt iodination laws. I just fail to see how market mechanisms can accomplish this in a state of anarchy.