Oh, and that entirely depends on the state. Health care would fall under subsidiarity, meaning that a private system would be preferable to one that is state run, for both efficiency and productivity concerns.
I think that's certainly debateable. I don't believe the private sector runs health care more efficiently for example, and even if it did, there's nothing that says it can't be a nonprofit insurance system like Switzerland. Heck, a Catholic state might have some form of church-run universal nonprofit health insurance.