Homeopathy is a good example. For an uneducated person it sounds convincing enough and yes, there are doctors prescribing homeopathic pills. I am still fascinated it still exists.
That’s actually a example of sth different. And as it’s basically a placebo it only harms people’s wallets (mostly). That cannot be said for random llm failure modes. And whether it can be prescribed by doctors depends very much on the country