Quite right, but at least if testing is widespread we would have more of an idea how the infection has spread and who is likely (or not) to be immune from getting it again. It would also help to get the mortality rate known more accurately so that the risk can be properly evaluated. At the moment we have literally no idea how many people have it or have had it in the past so the mortality rate is completely unknown - it could be 1% or it could be 13% (Current "rate" is 19,000 from 143,000 infections).