I personally think the way your question is framed is kind of an example of how insidious the influence of the current system is.
It's not a matter of "are there enough humans who have sufficient training in medicine who are willing and able to fill all those positions?" It's are there enough humans with sufficient training in whatever positions there could be to meet the health needs that exist?
Just for example: it's pretty clear many things done by physicians could be done by other providers, like pharmacists, psychologists, dentists, optometrists, if we broadened our idea of what those specialties (and their subspecialties) could look like. There are also probably types of providers that could exist that don't exist at all now, that we're not imagining because the healthcare system makes so many assumptions about what it looks like. Maybe all these things will involve additional training opportunities or whatever, but if you let people do what they are capable of, they'll find a way.
Sure, train more physicians. They'd be there. But you'll find even more people willing to do all sorts of things in ways we aren't currently imagining. We're constrained by convention.
Except that's the status quo. These days, all but the most intense of medical procedures is being done by increasingly less qualified people.
Nurse too expensive? Get a CPA!
Most of the time I go for checkups I see a CPA for the majority of the time, a nurse for less, and almost no time with a doctor. Excepts are usually for surgery or other intense operations.
This idea of "just let less holistically trained people do the work" honestly sucks. Dentists are better on average at teeth cleaning than dental cleaning specialists. MDs are better on average at putting IV needles in, etc
It's not a matter of "are there enough humans who have sufficient training in medicine who are willing and able to fill all those positions?" It's are there enough humans with sufficient training in whatever positions there could be to meet the health needs that exist?
Just for example: it's pretty clear many things done by physicians could be done by other providers, like pharmacists, psychologists, dentists, optometrists, if we broadened our idea of what those specialties (and their subspecialties) could look like. There are also probably types of providers that could exist that don't exist at all now, that we're not imagining because the healthcare system makes so many assumptions about what it looks like. Maybe all these things will involve additional training opportunities or whatever, but if you let people do what they are capable of, they'll find a way.
Sure, train more physicians. They'd be there. But you'll find even more people willing to do all sorts of things in ways we aren't currently imagining. We're constrained by convention.