If an economic system can't cope with a relatively minor external stressor - and Covid is not nearly as dangerous or destructive as some stressors - then the problem is with the economic system.
Actions do indeed have consequences - and trying to use the wrong tool for the job because you can't imagine a better tool is possible is not a wise action.
That's like throwing all doctors in jail and saying there is something wrong with our medical system because it not longer works.
What problems? There are no major structural problems yet. There will be major structural problems if OP's ideas are implemented because they're not sound. That's not related to the economic system, that's related to OP's ideas.
I'd argue that a 40% jobless rate is a major structural problem.
The real shame about this is that it's absolutely avoidable to a big degree.
At a cost? Sure, but I'd argue that it's exactly this, which a civilized society makes.
In what country? In the US, the unemployment rate is 11.1% right now?