I'm a doctor. I can tell you that even if I think a middle aged man with chest pain has anxiety he's still getting a full cardiac workup. Even a 20yo woman with anxiety will get a cardiac workup. It doesn't sound like these doctors missed anything based on this story. It sounds like they were ruling out the stuff that'll kill you quickly.
I don't see where we are disagreeing? I'm not arguing against triage.
GPs were mentioned - I'm simply stating that it's not uncommon that a patient comes to see a GP questions are asked to elicit the role of stress and anxiety in the situation as appropriate.
This does not rule out other care or take precedence over it as you know.
This is usually not true in most cases, it's actually something a good GP will explicitly consider by asking you the questions.
Maybe it was not possible due to something about your example, but it's recognized all the time in similar cases.
It's also a case for having a regular doctor in some form, because it's easier to recognize based on how well they know you.