Is there not a win-win situation through post-quantum homomorphic encryption? I'm not an expert in the area, but I imagine it's possible to set up a centralized system that contains pretty much all patient data for a nation, in a completely encrypted state. Then each institution/hospital could apply for access to make an application which generates only an aggregated metric of interest as an output, such as the map example given above, which could provide real-time notifications to medical personnel in the area.

I realize that many will come to say that the homomorphic encryption capabilities right now require a long time and many CPU cycles to compute some plaintext equivalent, but there would still be a huge improvement in the time required to be notified in the world today.

Additionally, performing studies in academia would likely be a far better experience if the data was available in a single place, and aggregate information could be gathered with a single API.