I don't disagree with you in the sense that the system is not sustainable (at least in the long-term) in its current form. But, in my opinion at least, it comes down to whether you want the burden to fall disproportionately upon individuals or on the state/society as a whole. The state has more resources to potentially raise revenue (even through potentially "unpopular" ways such as raising taxes, etc.) than a specific individual may, plus it would be more equitable for society by not implicitly forcing people back to work who feel uncomfortable working during a pandemic.
That said, there are definite limits to what states can do, and ideally support would come from the federal government which would have even more ways to raise revenue, not to mention the ability to run at a (even larger) deficit, if necessary.
I recognize that the status quo won't likely allow that in the near term. There aren't really many easy/quick/good answers as to what to do, but I do feel like putting the onus upon individuals to potentially choose between catching a disease and paying their rent in the midst of a pandemic is morally wrong.
For better or worse, I recognize that is a moral/economic/political calculation that everyone will likely make differently.
Sorry for the overly earnest post - I know it's not really the language of the internet