I'm afraid I do not see this part of the rule explained enough. Why is the identity important there? Wouldn't the content of the messages suffice? Often I do not even look at the name of the poster.
I believe the real explanation of why identity is important to them is a bit of social psychology. The theory is that identifying with people makes them less mean to each other. So they probably want consistent identities so people will be more civil, which is one of their stated goals.
It's also the way HN has always worked. A collection of nameless posts would be a very different kind of forum. Anyone is welcome to start one, but not to turn this one into that one.