Congratulations, President Obama. You have an important job; don't screw up.
I do frequently permit anonymous comments here, though, of course, I serve as the mediator and thus partial guarantor of their reliability and integrity. There are other contexts, too--for example, where fear of reprisal by the state is a real concern; or when feminists post about issues that are likely to excite the vicious misogynistic side of cyberspace--in which anonymity can be quite important. But as things stand now, anonymity is often abused on the Internet, so that individuals can behave irresponsibly with impunity, without incurring any of the social costs that would ordinarily accrue to those who behave that way.
Of course Leiter only gives examples rather than an exhaustive list; but it seems pretty clear that in most of the United States, the danger to pseudonymous speakers comes not from the state but from their employers and people in their profession. (Apologies to Leiter if he meant to include this category, but if he did it isn't clear from what he wrote.) Most people can be legally fired for almost any cause, including things they've written on their blog. There's even a word for getting fired because of your blog. Even if you don't get fired, your life might be made more difficult if your blog annoys prominent people in your profession; for instance it might make it harder to get a new job later. And these ill effects may not always be the appropriate ill effects of irresponsible behavior, because people may retaliate against speech that isn't particularly noxious. This means that almost everyone could have a legitimate fear of a quite substantial harm that might warrant keeping their online speech pseudonymous. For example, as I understand it Duncan Black originally blogged pseudonymously as "Atrios" partly because he was an academic without a tenure-track job who didn't want his blogging associated with his employer, so if he had been prevented from blogging pseudonymously (and there was in fact a frivolous libel lawsuit aimed at exposing his identity) we wouldn't have had one of the important early liberal blogs. I think that's a harm, though others may have different opinions.
This doesn't provide a decisive argument that the benefits of pseudonymous speech outweigh the harms. (The harms being discussed aren't the usual silly trolls on comment threads -- I don't even know if that's more common among pseudonymous posters -- but people posting harassing and defamatory things on, say, bulletin boards about college campuses.) But it does provide a bigger weight on any decisions people might want to make about the merits of pseudonymous speech in general, and in particular whether it is a good idea to expose pseudonymous bloggers. Leiter says "That someone chooses to blog anonymously creates no moral or legal obligation for anyone else to honor that choice," and while he's surely right about the legal aspects (and I have no idea what the legal impacts of the factors I've cited are), the justified fear of retaliation by private actors might give us pause about the moral propriety of exposing a pseudonymous blogger in many cases.
I should say that I literally don't know anything about the cases Leiter mentions in which he learned the identity of commenters or bloggers, other than what I read in his post.