Sadly, even countries with universal healthcare systems don't have universal health informatics systems (the NHS is a prime example — they spent £12B trying to build an integrated system [1]). Lots of countries attempt, including the US — HIPAA was actually originally about data portability [2], and we just spent another $40B [3]. Thus far only smaller countries have had success with integrated health IT systems [4].
[1] https://en.wikipedia.org/wiki/NHS_Connecting_for_Health [2] https://en.wikipedia.org/wiki/Health_Insurance_Portability_a... [3] https://en.wikipedia.org/wiki/Health_Information_Technology_... [4] https://en.wikipedia.org/wiki/Healthcare_in_Denmark#eHealth