Actually it is not anonymity that makes Reddit (or HN) successful. It is pseudonymity. You still have an identity, and the identity has value - karma. It is just disconnected from your biometric, "real life" identity.
The desire to protect the value of the pseudonymous identity is a powerful motivating force for making positive contributions. In many ways it is even more motivating than for your real life identity, because your real life, "biometric" identity is so precious that you will almost always favor low-zero risk contributions which are incredibly boring.
If Reddit was only anonymous it would be a horrible failure.