Well, there's definitely some generational gap here. I've heard of family doctors (though not once in a context of them not being a hilariously old-fashioned concept), but I've no idea why Mr Dog is terrified to see he may meet new people in the waiting room, aside from the basic fear of change.
Do pluggers even visit clinics? I think family doctors are supposed to visit you at home.
But I'm fairly sure if you had one doctor, then got a new one when the old one died, then had that one for the duration of his entire career, and all this happened back when people had a family doctor, and you're still alive now, that'd make you at least two hundred years.
Why does "Plugger" so often mean "Old"? Consider the main writer of the strip: A gestalt of the collective newspaper reader, expressed outwardly as its level of enthusiasm for reading the newspaper. The meaning of Pluggers shows demonstrably that newspapers need to attract a younger readership if they're going to avoid the fate of the dinosaurs.
Your humble critic's plugger status: I'm not, nor could I ever have been, nor will I ever be a plugger today.