If the government can provide effective healthcare that should at least in theory be a great boon to social mobility and entrepreneurship as that means people can much more easily move to a new job. Tying healthcare to employers is antithetical to that.
I suspect the real issue doing that in the US is simply because it's so varied. You've got several individual demographics within America that are bigger than Sweden's entire population - all with different cultures and even histories. Having a more homogeneous culture is advantageous in that respect. Maybe it's not surprising that SK has seen similar results.