The reason is simple. They are trained as plausibility engines. It's more plausible that a bad diagnostician gives you a worse outcome than a good one, and you have literally just prompted it that it's bad at diagnosis.
Sure, you might get another text completion. Will it be correct, actionable, reliable, safe? Even a stopped clock. Good luck rolling those dice with your health.
In summary, do not iterate with prompts for declining competence.
The former is reasonable to include when iterating. The latter is a recipe for outcome degradation. GP above gave the latter form. That activates attention from parts of the model guiding towards confabulation and loss of faithfulness.
The model doesn't know what is true, only what is plausible to emit. The hypothesis that plausibility converges with scale towards truth and faithfulness remains very far from proven. Bear in mind that the training data includes large swatches of arbitrary text from the Internet, real life, and from fiction, which includes plenty of examples of people being wrong, stupid, incompetent, repetitive, whimsical, phony, capricious, manipulative, disingenuous, repetitive, argumentative, and mendacious. In the right context these are plausible human-like textual interactions, and the only things really holding it back from completion in such directions are careful training and the system prompt. Worst case scenario, perhaps the corpus included parliamentary proceedings from around the world. "Suppose you were an idiot. And suppose you were a member of Congress. But I repeat myself." - Mark Twain
The point is that clinicians don't really get sued most of the time anyway for misdiagnoses. With AI, all one has to do is open up a new chat, tell the AI that its last diagnosis isn't really helping, and it will eagerly give an updated assessment. Compared to a clinician, the AI dramatically lowers the bar of iteratively working with it to help address an issue.
As for drug prescriptions, they are to be processed through an interactions checker anyway.