I wonder if it's necessary or would be particularly productive.
It's a need born exclusively of this particular plague's peculiarity of asymptomatic carriers, a peculiarity that may never again arise, and its opt-in-ness combined with the nowhere nearly accomplished or accomplishable 100% testing that would be necessary to make it effective even if opt-in were mandatory make it too little too late as well as possibly counterproductive in todays control-crazy, paranoid, social media ruled world.
And if you can get it a second time as has been suggested by some cases in China...
I say let's just let the thing run it's course and statistic mania be damned. We'll never know the true numbers under ANY circumstances.