Ok, but yes, I suppose that does suggest that, for personal emergencies, the office won’t be too overloaded with personal emergencies to deal with all of them.
How often would the latency of getting to the office matter? I’m not sure.
If the latency of getting to the office matters, the teacher is already using the intercom to tell the office to phone in paramedics, and get the school nurse in to the classroom immediately.
I can't imagine any vaguely-plausible situation where calling parents (rather than the cops and/or paramedics) is the correct thing to do IMMEDIATELY and first. (SOP is for parents to tell the school about their kid's medical issues so that if they happen during the school day, their schoolday guardians will not be caught unawares... so "calling the parents to ask them what the shit is wrong with their kid" when the kid is in the middle of some serious medical issue isn't even vaguely plausible to me.)