Your argument would be good, if LLMs got it right. But they will just as happily inform you that drinking your own urine is good for you, if you ask them in the right way. A doctor will always tell you no. An LLM will inform you about the dangers of vaccines and how there are many sources that say they give you autism, whereas a doctor won't.
Getting validation from the lying machine is not a way to do healthcare. The LLM confirming that you have some condition will not change anything, just like me and my forum buddies all self-diagnosing autism, and ADD doesn't actually help and actually causes a lot of harm.