Counterpoint, some doctors will zoom in on the most likely problem and misdiagnose. This is in part due to pressure on the health care system (where I live anyway); you can only get a GP appointment for 10 minute blocks, which really isn't a lot.
But when a 30-some year old shows up at a rheumatologist with joint pain they will likely go to unusual (at that age) but not unheard of rheumatism/arthritis, not hypermobile spectrum disorder. When a woman goes to a GP with period pain they will be prescribed mild pain killers or anticonception pills and fobbed off, until a decade and much suffering / many more issues later they get diagnosed with endometriosis.
You can’t run expensive, time consuming, and potentially harmful tests on every patient. Someone comes in with a headache, you tell them to go home and take an aspirin. You don’t send them for a a CT scan.
If it doesn’t go away and they come back, you start considering more serious issues.
It’s expected that uncommon non-emergent diseases will be diagnosed over multiple visits.
I think endometriosis is common enough that it would be caught earlier ("Oh, does your joint pain get worse right before you menstruate? Tell me more"), but your point is reasonable.
I counter with the platitude that common things are common - especially in fields like primary care, the amount of wasted effort one would expend in pursuing unusual explanations for every presenting symptom is considerable. We thus have to examine patients over time and trust that they will tell us if things have indeed not followed the course of the initial diagnosis.
Indeed, I didn't mean to imply that all doctors possess that skill in great amounts (or that, in any case, circumstances allow for full utilisation of the skill even if they do) or that medical history taking is therefore always of the highest standard. Obviously some doctors will be better at it than others, or more at liberty to use this skill than others (as you say, I could imagine a GP who only has 10 minutes per patient won't be as keen to start with fully open questions as a junior doctor in a ward who can clerk patients somewhat more freely).
Note that this isn't too different from, say, how software engineers are expected to be good at, and make good use of unit tests. But most probably don't (either because they never really cared to fully develop that skill, or their organisations applied contrary pressures leading to tech debt). But it is a recognised skill.
My main point was that, it is, in theory, a skill that doctors are expected to train (or at least pick up on during their practice), and therefore the same prompting principles that seem to apply here in the context of LLMs also interestingly seem to apply to medicine and history taking when "prompting" and interacting with humans.