The USA has a socialized healthcare system, it's called Medicaid and expanding it was a big part of the Affordable Care Act. In some states, such as California, Medi-Cal (the state's name for Medicaid) is fully available to legal immigrants and practically fully available to illegal aliens as well, the latter just have to use the emergency department rather than schedule a physician's appointment.

Our system does however assume that highly capable persons such as yourself are able to not only able to afford medical care, but also to pay for the socialized programs for those who can't.