ZD,
“Hatzolah does have someone man the board 24/7 even on Shabbos and even if there are no calls coming in. Obviously that person could man the board even if no phone calls”
Manning the board means that they will pick up the phone IF THERE IS A CALL. When there is a call they answer because then there is a specific case of pikuach nefesh. How can you compare that to working in an electric company where you would have to be mechallel shabbos even if there was no reason to even think there is pikuach nefesh? (BTW health facilities have back up generators, they can’t rely on the lectric being immediately being restored)