Excellent idea, great concept!!!
It's not everyday medicine where you work on simple problems following a statistical approach - an appendicitis is more likely than a Meckel diverticulum, and a simple overeating is even more likely than both.
But there are complicated cases - not very often, but that's the one I like, and that most of the passionated doctors do too. Hell - I love such cases.
A quick story - I once had the chance to make a one-in-a-million diagnosis while working in the ER of a small hospital, around 2004.
A patient presented with a psychiatric history and a psychiatric diagnosis, but somehow it didn't feel right. I had this odd feeling when talking to the patient - no psychiatric symptoms of no kind. It seemed wrong. I ordered basic blood tests (checking for hyponatremia, etc), X-rays - all normal.
It was a bit late so I asked for the patient to be served a lunch before being discharged, deeply unsatisfied. Around 10 minutes later, the patient had a new episode - but this time it was in an hospital and I did not have to rely on eyewitnesses - it looked a lot like neurological problem, not a psychiatric problem.
After another round of blood tests (I don't like it when I don't know what's happening), brain scan, etc. everything was normal. I noticed the glucose was normal - it should not be, since the patient had had an hospital lunch (in my hospital it included marmelade, and all kind of sweet things!)
So I ordered a test to check for insulinoma (I'm weird, I know - its incidence is like one-in-a-million) because it made sense - and the test was negative.
At this time, I was just a medical resident - the seniors were a bit mad at me for having spent so much time (and costly diagnostic procedures) on what was proven wrong, and what should be wrong in the first place - because it is so unfrequent. And that's not what one is expected to do in the ER (fortunately, it was late at night)
Yet I wasn't satisfied, so I asked the patient to be transferred in the university hospital neurological department for further tests. Something was happening, we didn't know what, someone had labelled the patient "crazy" (not politically correct, but truth is psychiatric patient issues are usually less investigated) but there was something.
Guess what- weeks later I got a letter, they found it was a rare variant of insulinoma that our basic test did not detect.
That's one of my best moment in life !! That day I made a difference - I removed a wrongful psychiatric diagnosis and gave the proper diagnosis. Patients with insulinoma should not get institutionalized in a psychiatric hospital.
That's the medicine I love. Fixing basic problems is the job a mechanic.
The kind of medicine I love is unfortunately not possible with the current healthcare setup - and even with usual patients, because most people don't care. They want a quick fix.
This startup idea is just great, to take care of people who want the real deal. I wish you luck!!
I'm sure you will find great clinicians who will take going as deep as the rabbit hole goes to give excellent care.