I think the issue here is not that physicians "are not investigators" but more-so that the financial realities are in no way aligned with dedicating massive amounts of time to any given patient. Physicians generally bill around $300/hour in cash only clinics, so I think it's a poor allocation of resources to expect them to dedicate 100s of hours to a more obscure patient. PhDs are dirt cheap, better to hand the odd case study off to them and let those with clinical skills focus on being clinicians to the more typical patient.
I'm a unicorn. No one knows what to do with my diseases. I've been told, with absolute certainty, for 25+ years that my worst one will eventually go away.
Finding effective treatments are more the result of drunken sailor's walk thru the solution space, than finding a leaf in a decision tree. I believe (but cannot prove) that'll be true of all rare multi-factor diseases.
The key point, advice is to never stop asking for help. Someone, somewhere out there has the answer.
I am appreciative when medical staff is required. But when it's not, ruthless automation must be out into place to contain costs.
Automated triage systems are already used at intake for urgent care clinics. They suck, partly because GIGO.
The challenge would be in creating software that can intelligently interact with a patient to surface the actual facts.
Humans are infinitely variable and read and interpret clues that we've barely identified let alone figured out how to automate reliably.
But that doesn't mean it's not possible. Machines will, one day, do this BETTER than humans can.
They are, as you say, trained to arrive at a diagnosis to the best of their ability and provide treatment. A challenging diagnosis, however, is a fully-fledged scientific investigation. This is where clinical researchers (MD PhD) can really shine, but it's hard to apply this to individuals; the typical direction follows funding first, which may not be of much help to any given patient. At any rate, this approach ultimately does not scale.
My hope is that new tools (accessible databases, better data collection, and a dash of ML) will get more patients in front of the right pair of eyes more often. The situation with life-threatening diseases is bad enough, but there are also huge opportunities for improved quality of life from vague, nagging, or intermittent illness diagnosis.