One problem with this idea is that the coronavirus just isn't that severe. If the mystery treatment has a 5% rate of severe complications, then the cure would be worse than the disease. Even 1% might be too much: consider that not everybody will contract the coronavirus, and the people most at risk from it (elderly or with comorbidities) are also likely to be at the highest risk of complications from some novel drug. A 5% risk of serious complications isn't unusually high: thalidomide was around 50% for pregnant women.

If the coronavirus death rate was comparable with the Spanish flu - around 10% instead of 1%, and severe in young healthy people - we'd be a lot more justified in rushing through untested treatments.