In a post apocalyptic world, there is no medical school. Once your health staff is dead or too old to continue, you're on your own.
In a post apocalyptic world, there are no high tech factories to manufacture medical equipment. From complex machines to basic surgical masks and gloves, bandaids, morphin, syringes, vaccines, gloves, none of those are manufactured anymore in a post apocalyptic world. The factories have been destroyed. The skilled workers who knew how to operate the machines are dead or who knows where.
Okay, so let's say that your bunker for rich couples with a mini hospital also includes a factory to manufacture medical equipment.
Gloves and masks are made of plastic. Petroleum products. So let's say your bunker for rich couples with a mini hospital and full staff complement and a medical factory now also has an oil extraction operation and a refinery on site. You need petroleum engineers. These engineers have families and will expect to be well taken care of. Replacing the engineers with robots? You're gonna need a robot factory, built by humans. And so on.
See where I'm going? If you take this reasoning to its logic end you arrive at a full society.
No one can survive well in the long term without a modern society and all of its amenities, including government, public services, and taxes. Exactly all that would cease to exist in a doomsday scenario. Unless you are prepared to accept a standard of living worthy of the Middle Ages.
Every man for himself is a libertarian fantasy.