What I'd Like To See At The Sochi Olympics

The Sochi Olympics are in the social media sights right now.
This is good.
President Vladimir Putin's hateful stance on gays in Russia appalls me. His purported reasoning for it which includes their lack of contribution to the Russian birthrate is specious at best.
Many people are appalled and there's a petition to sign asking for the games to be moved to Vancouver.
This is fine and admirable. It would send a message as to our thorough disgust at this stance.
But I have an alternate idea.
A wonderful, beautiful, logistical nightmare of an idea whereby every athlete from every country marches into Olympic Stadium, Sochi waving a rainbow flag.
It would convey how wrong and out of touch Putin's stance is while showing worldwide solidarity against him and for the rich diversity of human life.
It would be difficult to organize, but it would be even more difficult for Putin and all who agree with him to ignore.