Yes, although we should allow for people to purchase private healthcare too. Having at least a voluntary UHC Registry would reduce bankruptcy, help small business, lower premiums (through increased coverage), etc. There is a reason that countries like the Netherlands, France, etc. are ranked better overall in this area even if specialized care is better here. We could certainly implement some free market reforms to reduce costs though, like allowing for importation of drugs or buying health care insurance across state lines.
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Also agreed (although why health insurance would be restricted/governed by state is beyond me).