Most doctors aren’t surgeons.

No, but most doctors do at least some procedures, often a lot more of them than you might initially think. I'm an anesthesiologist; I have to think, of course, but a lot of my job is doing (just like a surgeon's). Cardiologists do cardiac catheterizations, GI doctors do endoscopy, pulmonologists do ICU procedures, radiologists do interventions, OB/GYNs do surgery and deliver babies. Even pediatricians fix simple problems like nursemaid's elbow. About the only ones who never, ever have to touch patients are pathologists, psychiatrists, nephrologists, and endocrinologists. You could make a career in neurology, outpatient general medicine, heme-onc, pure diagnostic radiology, and a few other fields with minimal physical interventions if you wanted to, but most doctors do at least some.

No, but a GP can also not do those things and on top of that I've met some pretty terrible GP's :p

So maybe some classes of doctors are done...

Another thing to keep in mind: tons of people don't have access to any type of doctor at all (too expensive, too far away, queue too long, etc). Is current state of AI better or worse than no doctor at all? I don't know, but the answer is not obvious to me.

In those cases AI isn't competing with GP's, it's competing with internet searches.

A GP does a lot of hands-on work that is currently out of reach of a robot. And in addition, the interaction between the theoretical and practical parts of the job is quite complex.

With ageing populations in all western economies this is also needed as there won't be enough GPs around to service everybody.

Public conceptions of medicine are strange, especially in the US where almost everyone conflates physicians and surgeons.