Sorry... nationalizing stuff is not a panacea.
Who said anything about nationalizing anything? A real healthcare system doesn't have to be nationalised.
Take the Canadian system, as a prime example. As it is not something enumerated in either the constitution, or the British North America act before it, by default healthcare is under the jurisdiction of the provinces. Each province runs its own single-payer insurance system, and sets standards for care and outcomes. In turn, each province is divided into regional health authorities, which for the most part own and operate the hospitals in their region, as well as handle things like health inspections of restaurants, initial investigation of disease outbreaks, and so forth. In turn, unless they are on the hospital payroll (rare), doctors in turn are free to operate their practice as they see fit (private business, partnership, chain etc...) the only proviso being that they either have to be in the public system, or completely out of it, no double-dipping.
The net effect is that hospitals, and doctors are operated locally and in the case of hospitals, in a non-profit manner. This results in a reasonably efficient system that costs far less than the US system, while delivering similar or better outcomes.