China has until recently had a less socialized healthcare system than the US. They've made massive strides towards trying to provide a universal system over the last few years, but they are still a developing country, so I'm not sure why you think comparing with China is a good idea, other than, I guess a knee jerk (and incorrect) assumption that it'd all be government run...
Meanwhile socialized healthcare systems are working out fantastically well for large parts of the developed world, but really the most important factor is universal healthcare - universal systems range from fully private multi-payer systems with some system for subsidizing those who can't pay, to fully socialized single payer systems.
What the vast majority of them have in common is that they result in far lower total healthcare spending than in the US thanks to actually regulating healthcare with the public in mind rather than insurers and healthcare providers. In fact, a large number of countries spend less total on healthcare per capita than US taxpayers pay towards Medicare and Medicaid alone, before you even factor in US private insurance.
_You_ get healthcare as well. It's not just "someone else", it's you, your family, your friends, and everyone you care about. No one should go into a spiraling life of debt because they broke an arm or got sick at an inopportune time.
It's easy to think that China is run as a socialist country because there's "communist" in the name of the ruling party, but the truth is very far from that; in many aspects China is a ruthless capitalistic free-for-all society with less socialist policies than even the US.
It's actually very informative, to me. Sorry you don't see it that way.