I don't think slapping jingoistic labels like socialism advances the discussion much. If you look at the economies ranked the most free by the Heritage Foundation:
The top 5: Hong Kong, Singapore, New Zealand, Switzerland and Australia all have some form of healthcare subsidized by government.
Government is just one tool in the toolbox. It's not inherently evil or good. Depends on the job. Despite what combination of tools we choose, the goal should always be: to provide quality healthcare to all citizens.