To say that we have no mechanism to pay for unemployment or health care for the unemployed is disingenuous at best. The poor are exactly the people whose healthcare the government does pay for. And the CARES act largely just expanded existing welfare and unemployment benefits.
Perhaps you haven't spent much time on unemployment or Medicaid? I work in a dental clinic, and it seems like every month there's another wrinkle added to the Medicaid system to make it stingier and to chase away more providers. Unemployment only helps a quarter of those who are unemployed, and it pays those people on average a third of what they were making while employed.
This diagram shows that "CARES Act" was very much not about "expanding existing welfare and unemployment benefits". [0]
Americans who haven't traveled have no concept of how a functioning polity cares for citizens during a pandemic. If our government doesn't care for us, why do we tolerate it?