The point isn't to sway the emperor. (When the facts change, he changes the facts.) But there are many people answering to him who currently don't have the backbone to say no to him. Seeing a million people out there shouting that the emperor has no clothes on may give them that little extra bit of courage necessary to make the right choice in one of the many daily situations where they have the choice between being pandering yes-men and doing the right thing.