As the original Publius argued in Federalist No. 1, keeping one's identity concealed can force readers to focus on the quality of your arguments, rather than on personalities. It's harder to get ad hominem about a writer you can't identify. So a pseudonym can serve a good purpose in public discourse.
Of course, if the pseudonymous writer stoops to low or unethical arguments himself, it's harder to call him on it.
I don't generally read the National Review, because what passes for logic over there is migraine-inducing. For example, here's Matthew Franck, contradicting himself in the space of four sentences in an effort to defend Ed Whelan:
So, Franck's saying that pseudonymity forces the reader to address an argument on its merits rather than go after the author. But if the argument is a bad one, then it's harder to address the argument's merits so it's therefore OK to go after the author.
Huh. Franck thinks bad arguments are harder to deal with than good ones. I sense a little self-centeredness creeping in there. After all, Franck obviously knows a thing or two about bad arguments.
Yup. Here comes the migraine...