You can do authentication with the party you're communicating with as your real identity or as a pseudo-identity without letting everyone else know who you really are.

With PGP, just use an identity that identifies you to that party and sign your emails with it. It doesn't matter what address you send them from.

However, anonymous emails where you don't even authenticate yourself to the party your communicating with is also useful. It's like when someone wants to make an anonymous report to the police. Why leave a trace with the phone company? I imagine people that make these reports typically use street phones (in countries where they're still plenty).