in market equilibrium, should we expect two- or three month-long waits to see a doctor?
The alternative is for the doctor to charge more for a visit, thereby shortening the queue.
My guess is that this has something to do with the fact that insurance pays for most doctor bills. The insurance company is not the least bit inconvenienced by waiting, but it cares a lot about price.
The doctor cannot drive away patients incrementally by raising fees. Instead, if the doctor raises fees by enough to get taken "off plan" by an insurance company, the doctor loses a whole bunch of patients. So the choice for the doctor is either having a long queue or risk having lots of spare time.
If my hypothesis is correct, then we should observe shorter queues for doctors who do not take health insurance. I am not sure if this is the case. I know that "boutique medicine" is a way for patients to ensure short queues by paying the doctor what amounts to a retainer fee (on top of fees for individual visits--although sometimes an annual checkup is included in the retainer). If you tried to use the "boutique medicine" model for the whole country, you might need three times as many doctors as we have now.