If you wanted to know how Covid was moving through the population that wouldn't be a valid way to count. If you wanted to know what it's actual lethality is that's going to introduce errors.
But wasn't the point learning about a virus which was entirely new to the human population? In that case it seems reasonable to me to gather as much data as possible and fully analyze it once the emergency was over.
Are we still in an emergency situation? Were we ever all in an emergency situation? Often in life that wisdom comes in retrospect.