> Many medical facilities are only staffed with permanent nurses, with doctors helicoptering in, from time to time, to take care of specific duties that may require certain licenses, or provide specific advice.

Maybe for a very loose definition of medical facilities that includes assisted living facilities.

But for example in an ER, nurses come and go with very rapid turnover and it’s common to staff with temporary travel nurses.

> nurses tend to do most of the actual work

Techs, environmental services, phlebotomists, respiratory therapists, CNAs etc. probably do more of the “work” than nurses.

> highly experienced nurses actually taking up the mantle for many duties often done by doctors

Only if they go back to school and become a Nurse Practitioner or CRNA, but in that case they are no longer functioning as a nurse. Even then they are general operating under the direct supervision of a physician.

> Nurses are in far higher demand, than doctors.

Only in absolute numbers. It’s far harder to hire a doctor than it is a nurse. I know an ex-NFL player who works as a physician recruiter.