A risk would be, that if you find an exchange now, which does not demand an ID .. the question will be, what about the moment you want to cash out?
Things can change very fast. The exchange which is open for everyone now, might not be in the near future, once authorities have put pressure on it.
But what about if you only want to change some fiat to bitcoins and put to youre own wallet? This cant take long time. And giving him youre ID didnt asure you that you can cash out. In fact is a security factor for exchange from you, no to you from the exchange. They can go away with your cash and youre ID an then...whar?