Controversial title but here's why: With the ability to use nicknames, you can delude yourself into thinking you have privacy when you really don't. With a real-name policy you are having your lack of privacy rubbed right in your face so you don't forget it and do something stupid under an "assumption" of privacy.
You want real online privacy? Don't use Facebook.
You think this violates the "anonymity" of the Internet? The Internet was never anonymous.. it's just that the Internet made it (and still makes it) difficult to verify that the other person at the end of the pipe is actually who he says he is and isn't lying to you. Don't confuse lack of authentication with privacy, they ain't the same thing.