I don't disagree with what I interpret as the intent of your message - that there is real value in process, question repetition, and not jumping to conclusions.
I do think it implies a false choice at the end though. A doctor can imply they care / listen / are familiar with your case, while still asking insightful questions and probing for relevant changes.
[Analogy] As there are many engineers here, consider this contracting example: how would most companies respond if, for a project, at each meeting, the contractor sent a new representative, who asked all the same questions as the first meeting, could provide no status updates, and many reps suggested apparently different solutions, platforms, or approaches?
This is an important point but I feel you're approaching it from a very short term view. Look at Pakistan, for example: after the CIA used a vaccination program as cover for a genetic testing scheme meant to find Bin Laden [1], there was (and still is) a significant impact on the Pakistani and other population's trust in their domestic healthcare industry [2]. Even if it was a real Polio vaccination program that saved thousands of lives in a purely utilitarian short term calculation, the damage that distrust causes long term can far outweigh the benefits. Worst of all, due to the nature of that distrust, measuring that damage becomes so much harder.
The point is, doctors don't just need their patients to trust them, but to trust the institution of modern medicine and healthcare as a whole. They need the patients to trust their nurses, pharmacists, specialists, and technicians just as much as the primary doctor. Given how critical patient cooperation/honesty and preventative care are to clinical outcomes, I don't see any convincing evidence that patient perception isn't just as important as the rest of the process.
[1] https://www.theguardian.com/world/2011/jul/11/cia-fake-vacci...
[2] https://www.scientificamerican.com/article/how-cia-fake-vacc...
More often than not, if I got someone on the other line that seemed to know a bit, skipping the questions ended up being counterproductive, as I would assume some knowledge about a specific item from the other end that didn't exist (but other knowledge did). I learned to trust the process, and glean the extra bits of information that weren't what the other side was trying to convey, but did nonetheless.
I think it's a mistake to assume that just because the doctor asks you questions and doesn't always seem to take into account a prior answer the doctor is not listing. I think it's more likely that they have learned that the small percentage of time that asking similar questions in different ways has led to new, important information has led them to be careful and methodical, even at the expense of patients thinking they aren't listening.
When faced with a choice of behaving in a way making you think they care, or behaving in a way that makes you think they don't but actually provides better care and outcomes, what would you prefer? I think we need to be careful about jumping from "this is what it looks like" to "this is what's going on" without evidence clearly pointing to one over that other.