I can write and sell books advising you to treat your cancer with organic kale and meditation. Following that advice will literally kill you. But I can't give you a tour of the national mall, because... Because what, exactly?

You can't protected all the people all the time, it's simply impossible (or would result in a dizzyingly oppressive Brave New World style situation). At some points, people need to take responsibility for what they do to themselves/let other people do to them, even if some people might suffer a chemical burn from a back alley untrained hairdresser occasionally as a result - just like people do all the time when they try to do these things to themselves at home, which of course is perfectly legal and not to my knowledge a source of many calls for licensing of the ownership and operation of a watertap and a plastic bucket?

Also, licencing hairdressers doesn't even prevent fuck ups from happening there, that's people with nontrivial haircuts (the group of hairdresser clients formerly known as women) pay so much for haircuts. They know that they're hard to get right, and that it matters that the hairdresser knows what they're doing. This is equally true in jurisdictions where hairdressers are licensed and where they are not.