You're missing the secondary costs. What are the costs of people having to sit at the hospital all day waiting for the doctor to see them. And what are the costs of people putting off seeing a doctor since they can't get an appointment?
Since, right or wrong, people want to see doctors rather than nurses when they bother to go into the hospital in person
Only if the 'costs' are them same. If you just ask people when they come in if they want to see a nurse (short wait and pay $X) or a doctor (long wait and pay $3X), I think you'll find many people opting for the nurse.