I (if I controlled the government) would have done the same thing the government does during a bad flu season.
If I also controlled the government I would likely use the crisis as an opportunity to turn the health care system into a completely decentralized blockchain aided free market system.
If it was truly a bad pandemic people would be able to buy respirators (or 3D print their own), have a negative pressure room in their home/garage/basement, and AirBnB the hospital space. Uber Doctors and Nurses that come and check on patients and give monitoring advice to AirBnBs.
While I have also been control of the government I then turn every law enforcement agency into a blockchain based P2P service where if you need a threat managed you get on your app which uses AI to automatically contact the closest threat managers to deal with your particular situation until a private investigator can come in and gather evidence which is then utilized for an Augr type of trial to determine if the victim requires compensation from the accused.
After being given such supreme power over the government I would work until my position is no longer necessary and the market has fulfilled all roles from my central place of authority down to the smallest individual.
During the Spanish Flu, many local governments mandated people stay in doors or wear masks when going outside -- that's what the government did during a really bad flu season. Regardless, covid-19 is more lethal than the flu and doesn't have a vaccine. Nobody has natural antibodies built up against this virus.
Your approach would only work for the wealthiest 10% of the population. Putting everybody else on their own would inevitably cause a problem for those 10%. Regardless, your opinions are an interesting way of looking at things, so thanks for answering my question.