I can't help but think that the medical system feels something like a mix between an aristocracy and a cartel.
On one hand, it seems very much a class-based system. Doctors aren't involved in a lot of hands on medical practice, they get nurses to do a lot of it. Is this a specialty based division of labor, or is it a remnant of a class system from a couple of centuries ago where doctors were likely to be members of the social elite from birth?
On the other hand, there seems to be a lot of cartel like structure that's designed to limit competition. Filtering structures in training and education serve to limit who gets into medical school and who is able to finish residency. And by limiting the number of people who can be doctors, you are able to justify a class based labor system, high wages, etc.
Then there's the actual practice of medicine, where only doctors are allowed to do a fairly wide number of medical tasks or have to be involved in supervising non-doctors whose training would seem to make them reasonably qualified to do on their own.
Another poster in the comments suggested we need more, less well trained doctors. That's probably reasonable. Other than an emergency surgery I had a couple of years ago, I can't think of much of my exposure to the medical practice that couldn't have been met just fine by a nurse practioner or physician's assistant. Sure, we probably need the specialists and people with advanced education for diagnoses and speciality care -- your level 2-3+ ticket escalation -- but it seems like for the majority of ailments and regular care, a doctor is simply overtrained and underavailable.
And what about pharmacists? They have doctor-like training yet for the most part don't seem to do very much but count pills. Sure, they serve as a safety net in some regards to make sure that people who take a constellation of medications don't end up with complications from contraindications and side effects, but that's limited to a person getting all their prescriptions filled by one pharmacy, which is habit people have, not a requirement.
If you think about it, even with the class-based structure of medical practice, today's physician assistants and nurse practitioners are probably better trained and more informed than most general practioners were 50 years ago. It's not hard to see why it wouldn't make sense to have PAs and NPs make diagnoses and suggest drug therapies that could be vetted by pharmacists with a more detailed knowledge of drug efficacy and effects.