I'm not sure that is true. I think that US has had private healthcare for so long that they can't really consider a system that is radically different. Where children are taught that they should practice sports as part of an strategy to lower healthcare cost. And that getting regular checkups is good. Or that banning smoking in public spaces makes sense to reduce cancer treatments. There you have a synergy between public education and public healthcare.

Is not so much about planned economy than about teaching some habits and passing regulations to improve public health. Next would probably be try to lower contamination at cities (bad for the lungs). Is a completely different way to see things but makes perfect sense if your aim is to reduce global (country) cost.