A guaranteed way to further screw it up (our health care system) is to turn it over to bureaucrats. And that's a good reason to do look into ways or organising a comprehensive health system that wouldn't do that.

But isn't your present health service largely run by bureaucrats already?   "An official who is rigidly devoted to the details of administrative procedure." Sounds familiar? For example accountants and other deskbound people working in insurance companies and hospitals.