what would you program into the ideal robot nurses/doctors

Your heading and post are about different things. Robot or real doctors and nurses?

If I was programming a robot, I would include a way for the patient to contact a real breathing, speaking, listening human being who would observe my expression and tone of voice as I described symptoms and asked my questions, someone who would make conclusions with that information as well as the bare facts. He or she would explain the diagnoses, treatment and prognosis in terms that I could take in and understand. Robot chats usually bring you round in a circle that starts back at the beginning again without properly answering you

I don't know enough about all the individual specialists who might be able to help with every ailment I might suffer from. I rely on my GP to refer me to whoever is most suitable for the problem of the day. Since I won't be travelling (expensively) round the globe for (expensive) treatment, that will be a relatively local consultant.

Thx for taking the time to reply. As a (retired) human being health professional, I appreciate your preference. But... AIs will be able to assess much of what you described and refer you to the best humans for you. And to be kind or even funny (your preferences). Eg, I live in America, so I just asked an AI to list the best surgeons for an issue and it checked my insurance (we don't have NHS) and listed the best "peer reviewed" surgeons, with their contact info. This feels like the most basic guidance, What else might someone want? Monioring my meds would be nice!

What else might someone want?

An orthopaedic waiting list that doesn’t involve a wait of a year for a total knee replacement classed as urgent would be beneficial. AI might well be able to suggest the best surgeons but that’s not much help with the current state of the NHS.

Compassion.
The abilty to take heed of what they're told., by the person who has taken the time to make an appointment.