Staying home is productive though. It slows the spread of the virus and adds value (in terms of capacity) to our hospitals and healthcare system. You can think of unemployment benefits as the government purchasing that time from employees and instructing them to use it in the most valuable way to us as a society: do nothing.

The person's time is valuable (and so they should be compensated) but the most valuable use of their time in the short-term is to not use it at all. Tech does this all the time. We just call it "rest and vest".