The USA has been making plans for widespread sharing of Electronic Health Record data for many years:

https://www.healthit.gov/hitac/committees/health-it-policy-c...

This is seen as desirable for more than one purpose, including allowing people to move their medical records to a new doctor or hospital easily, and for doing research on what makes for the best care, as well as giving doctors the ability to look at case histories similar to that of a patient they are treating.

Computerization of medicine has been resisted by doctors for a long time, which has meant that all the data and observations and diagnosis made over the years has essentially been lost when it could have been informing doctors decisions and being used in research. There are definitely privacy and abuse problems with putting everyone's health data in a central database run by the government, and it is very difficult to de-identify health data (how many people have your height, weight, age, and diseases?), but without some way to gather all the knowledge and experience and data from the practice of medicine we have been missing important correlations and creating harm due to each doctor making their own decisions instead of having a set of best practices informed by hard data. Whether the police, FBI, NSA, courts, and politicians should have access to this data are difficult questions and hard to implement so they are not subject to abuse. The police already can make some kinds of queries at hospitals for medical data.

The UK has started a large scale Precision Medicine project that is collecting health data on 500,000 people:

https://en.wikipedia.org/wiki/UK_Biobank

There are other ongoing large scale projects collecting health data also:

https://www.hdruk.ac.uk/

and I'm sure there are others, in many countries. A lot of this is part of the move towards Precision Medicine, medicine based on data and personalized to an individual, rather than treating all people as being identical and letting each doctor make their own guess on how to treat a patient (I've been in meetings where doctors say that 80% of the time they are guessing, though guesses get better as they see what works and what doesn't for any one patient):

https://en.wikipedia.org/wiki/Precision_medicine

The space Apple is aiming to dominate is currently one small part of all this. One big question is what do doctors do with all this data? It's too much to look at it all. They have no experience with such detailed info also. What is normal for the way your blood pressure changes as you go about your day? Your doctor doesn't know and hence even if she had continuous blood pressure measurements from you 24/7 wouldn't know what to do with it. What is a reasonable blood pressure while having sex? When climbing stairs? The only measurements like this that we've had historically are from astronauts.
Machine Learning may help, but what do you do with an opaque message from an algorithm that there is a 75% chance you have some abnormality in some obscure biological parameter? The chance of 25% of those notifications being wrong means you can't use it as the basis of a diagnosis. Maybe it suggests something you can investigate further, but then how much time will you waste following up on those 25% of notifications that are in error? Was the ML trained for your age, weight, and specific set of health conditions or will it fail to detect anything for people outside the scope of the training data, yet be used to evaluate your health (incorrectly) anyway? And using ML also creates yet another path for bad actors to steal and tamper with your data.

There are a lot of complicated questions surrounding medical data.