It is true that docs are slowly being replaced to a certain degree but not by robots.
Nurses: getting more and more responsibilities
Nurse Anesthetist: although they are required to work under the supervision of a doctor, many hospitals are "supervising them under the chief of staff or whatever and they are replacing Anesthesiologists (recently there has been some cut backs on what these nurses can do, but it is still frightening)
Naturopathic Doctors: (ND or NMD)These guys can actually prescribe medications, order labs, and do minor surgery in 13 states (and it is growing). They often call themselves "naturopathic medical doctor" and say they have gone to "medical school".
Physician Assistants: Slowly they are gaining turf, they still have to have a supervising physician but they are taking the responsibilities that only docs could do 10+ years ago.
Psychologists: Currently they have gained prescribing privileges in 2 States. They are gaining more turf and are taking over privileges only docs had a few years ago.
Chiropractors: They are considered primary care physicians in many states and can bill insurance, diagnose, and they are fighting for prescription rights.
Optometry: They have prescribing rights and are fighting to do surgery in many states, and have taken many of the ophthalmologists patients. The public often has no clue that an Optometrist is not a medical doctor, but a doctor of optometry.
Podiatry: Can prescribe and do surgery, etc. Many foot surgeries that were mostly done by orthopods are now common place podiatry procedures.
Doctors in other countries: right now there is big talk in radiology that many of their practices (reading MRI, etc) are eventually going to be farmed over the internet to doctors on call in India. These docs in India will do this for a lot less money.
I could go on but I think that you get the point. I would not be so worried about robots, however I guess some of this technology could cut out some of a doctors responsibilities, but the reality is other fields are replacing doctors. I think there will always be a need for MD/DO physicians but it is frightening how much turf has already been taken. I am not talking down on these other professions and I am not trying to flame them at all. I am just talking about the reality of doctors turf / responsibilities slipping away.