> What I'm proposing is an intermediate step between doctors and nurses (or perhaps buffing up the powers of higher level nurses so they could operate standalone)

We have categories matching that description in the US now, most notably Physician Assistants [0] and Nurse Practitioners [1].

[0] https://en.wikipedia.org/wiki/Physician_assistant

[1] https://en.wikipedia.org/wiki/Nurse_practitioner