One issue I can think of is there is selective pressure on viruses for them to become less lethal over time since killing the host is counter productive. You can't compare now to the past for death rates since as the virus spreads and mutate the pressure is to become less lethal.
If you want to compare the effectiveness of a drug on a virus you need to compare in the same population and random is really the only way to do it since you need to make sure that the mutations you are dealing with are in your test and control populations.
I wish we did not have to do it this way since a lot of people die as a result. I wish we knew more about how our bodies really worked so we did not have to do this. However we don't. We are learning quickly but we are not there yet. If we don't do random drug testing then more people will die in the end and the process will take far longer.