The government recognised there is a public health issue in school vaccinators/GPs having up to date info on immunisations, so they could schedule vaccination programmes and quickly know where low coverage rates existed in case of an outbreak.
So - the school carries out vaccinations, and the details get electronically transmitted (using HL7 protocol) to a central register managed/hosted by the ministry of health. Similarly, if a kid goes to their doctor and gets a jab there, the GP uses their own local system to query that register, download details of other immunisation events, and add ones they do there. It all syncs with this central register, and seems to work very well.
That way, in case of an outbreak in a particular region, they can easily know who is at risk and send nurses into a specific school to notify teachers and parents.
This is the *only* use case other than allergies I can imagine schools needing any contact with medical info, and even then - they should not be storing it locally or via any kind of cloud site, if an effective solution like this can be done in a small country like NZ. Is there a reason something similar couldn't be done centrally in the US, with federal/govt money or is the system that deregulated?