Diagnosis is just a small part of a doctor's job. In this case, we're also talking about an ER, it's a very physical environment. Beyond that, a doctor is able to examine a patient in a manner that isn't feasible for machines any time in the foreseeable future.
More importantly, LLMs regularly hallucinate, so they cannot be relied upon without an expert to check for mistakes - it will be a regular occurrence that the LLM just states something that is obviously wrong, and society will not find it acceptable that their loved ones can die because of vibe medicine.
Like with software though, they are obviously a beneficial tool if used responsibly.