There are already AI assistants for doctors. But the demand for healthcare is unlimited, so salaries will probably remain high and job markets tight.
The few times I have been to the doctor it has seemed like relatively standard knowledge work, gathering information and reasoning based on known and unknown factors.
The differentiating factors that make it high status and difficult are seemingly the same as for most knowledge work jobs: high stakes, high stress, high knowledge and skill requirements, limited pool of qualified people.
So unless I am mistaken, it seems like the kind of work that is very suited for automation. At the start it could be as simple as an AI automatically summarizing patient meetings.