People can survive quite well without the care of physicians.
I am not a doctor (but will be in a few more months
In this matter, you are certainly correct. In the past (and in some places, even today), there were human settlements in which there has never been a doctor -- at least not in the modern sense of a doctor. And for the most part, life went on. Humans managed to be born, grow up, and grow old. Occasionally those lives might be cut a bit shorter and harder than otherwise -- but on average, these occurrences were infrequent enough that we could be assured the younger generation would survive to repeat the next turn of the cycle.
Yet, in each of those villages, you would find a healer. A shaman, a medicine-man, or maybe some weird old lady living at the edge of the settlement. Sometimes their herbs and potions would actually be useful; mystical incantations probably somewhat less so. Regardless of how primitive these healers were, they would be summoned to offer up what they could. They were a source of comfort that could be turned to, when a loved one was sick or dying. And they were also one of the few educated people (whether formal education or by traditional teachings) in the village that could be turned to for knowledge and advice (clergy being the other major source).
Many of us on Slashdot do not have families of our own, or at least that's the stereotype. We often have only a dim understanding of what illness can do to the structure and functioning of a marriage, a family, a clan, or even an entire village. When people don't understand what is happening and begin to fear, when they believe nothing can be done and begin to despair -- the social bonds that hold us together fray and rip apart. This dynamic is why healers exist and are so highly valued in society, even in a modern age where miracles are commonplace and expected to occur on demand. And why post-apocalypse, they will continue to be valued.
That being said, I would agree that some doctors would be more useful than others. Rural Medicine, Wilderness Medicine (an uncommon specialty), General Surgery, and Veterinarians would be the most immediately useful. As for the rest of us, at least all doctors go through medical school and internship, have studied anatomy and physiology, dissected cadavers and such -- it might take some retraining, but it should be possible to get at least the more adaptable ones back up to speed on how to remove an inflamed appendix or gallbladder, perform a Cesarean, or set a broken bone. As for our other skills -- the skills of compassion, comforting, and guidance -- hopefully they practice these most basic Physician's skills on a daily basis (although sadly enough, I know not all of us do).