> Increase nurses, allow them to get promoted to doctors.

I think this sentence shows that you don't really understand the difference between the two jobs. Nurses and physicians have wildly different training/education. There are things about the body that any first year medical student could tell you, that nurses never learn even after decades of experience (because they don't need to).

> Increase nurses, allow them to get promoted to doctors.

We already do this.

https://en.wikipedia.org/wiki/Nurse_practitioner

So one problem with a nurse -> MD career track is that they are just fundamentally different roles. It's not (just) number of years of schooling, but what they study. Nurses don't do diagnoses or prescriptions, and don't receive much if any formal training in those areas. So I'm doubtful you can make up that difference with just on the job training (though doctors who were once nurses might be better doctors).

That said, I think that a RN -> NP career track with some kind of "executive NP" program (analogous to "executive MBA"), followed by supervision under an MD and eventually graduating to full autonomy, is an interesting idea.