PBA
“Doctors put on their work clothes, go to their regular job. While their kids sit at home and mother yells at them.”
Thats true for Some. (though exceedingly rare that it would be every week)
Others carry a phone answer emergent/urgent questions
Others carry a phone answer urgent emergent questions and occasionally go to the hospital if/wwhen their is an emergency (this is the group that is similar hatzola)
still others dont even carry a phone (see DY’s post)
Thus your line “Except doctors don’t keep shabbos.” should read “some”
(as an aside Sadly though some accountants, lawyers, mechanics laundry chute sweepers and Elephant trainers also dont keep shabbos. (granted not as many as doctors ))