As I said before, I am friends with a few and at a recent baby shower, I asked the question about why they don't agree as part-timers to share a part-time position and patients. To me as an outsider, it seems logical that one doc covers mornings, the other covers afternoons and they can switch it up to fit each others schedules/needs. This way, there is always coverage each day for patients. I was laughed at and then told that it would never work and that each provider is different and wants their patients to be their patients, etc. What was missing there though (that I DID not say) was that the patient's needs come last.
I think your question was totally reasonable and they shouldn't have laughed at you. Maybe they each want to work only during school hours and be home the rest of the time. So there is no way they could do a job share because they all want the same shift. But surely there are other ways the clinic could accommodate the part-timers. Job-sharing is the simplest, but if that won't work, they could explore other options to make sure someone is available to cover patients when their primaries are not there. That is, if they are interested in improving their customer service.
I hope your former pedi has a better attitude than your friends.