Consider this angle. If a doctor in a socialized healthcare system knows that he is not going to be properly compensated for the work that he does, then that doctor has no real incentive to offer his services. This doctor might move to another state which would allow for him to make more money, or he might decide that being a doctor where he is now isn't the best of jobs and might consider another career choice instead. Either way, that is one less doctor providing medical service. Even if the number of patients stayed the same, with fewer doctors, delays would have to go up because there are fewer doctors to treat patients.
You are both correct in saying that below-market payments give doctors less of a reason to offer their services. As a result, when doctors offer fewer services, regardless of the influx of new patients, then the longer waiting times take place.
I’m just picking on the author for leaving out this crucial step in his argument.
And because of your input, I must revise my argument that it is only the influx of new patients that result in longer waiting times. When doctors offer fewer services, this also contributes to longer waiting times.