Looking at the Nordic countries you might possibly make the counterpoint that publicly funded health care implies a taxation model that makes it economically unrewarding to become an entrepreneur.
It's also not obvious that Nordic countries (e.g. Finland) have less entrepreneurship than the US does. If they do (I couldn't find hard data), it's as likely to be for cultural reasons as economic ones.
Scandinavia has produced a disproportionate number of artists and athletes - another kind of "entrepreneur." No doubt access to healthcare made it easier for them to pursue their passion.