In logic, an argument is valid or it is not. The truth of a conclusion depends on the truth of the premises and the logical validity of the argument, and not on the identity of the arguer. "All men are mortal; Socrates is a man; therefore Socrates is mortal" is true whoever says it. When anonymous folk on the Internet exclaim that their identity is unimportant because "the truth of an argument doesn't depend on who makes it," what they mean is that the truth of a conclusion doesn't depend on who reaches it.
But logic is just one part of persuasion.
In rhetoric, the test of an argument is not whether it is valid, but whether it is persuasive. A logically valid argument based on uncontested premises may be persuasive, but so may a logically valid argument based on questionable premises or even, to the right audience, a logically invalid argument based on false premises. The other elements of persuasion, recognized for two and a half millennia,* are emotion and personality. A charismatic demagogue (character, ethos) talking to people who want to believe (emotion, pathos) might convince them of things that have no basis in fact or reason (see, e.g., every organized religion but yours.)
The internet has removed all barriers to mass communication. The cheapest way ever to reach large numbers of people is in the comments sections to popular blog posts and newspaper articles, where a commenter's thoughts might be read by thousands just because he has posted immediately after some highly popular post or article. (I've tried to think of a comparable mechanism, pre-internet, that someone with no credentials, no knowledge, no talent, no money, and no time could use to get the attention of thousands of readers, and I could come up with nothing lawful.)
Because of these low barriers we have millions of people yammering for attention online. The vast majority of them aren't exhibiting anything resembling logical rigor; they produce more heat (pathos) than light (logos). Now, I probably hope for too much from people, but I'd like to think that all of these words are to a purpose—to elucidate, educate, persuade, or entertain; or just to be heard.
Those who only want someone to listen (and who realize it) don't have any special reason to identify themselves: whether they are heard or not doesn't depend on the truth or the persuasiveness of their words.
By the same token, those who only want to entertain can easily do so from full anonymity. The following joke is awesome, whoever tells it:
The bartender says, "we don't serve faster-than-light particles here."
A neutrino walks into a bar.
Why? Because you don't need to believe any part of the joke—even that some neutrinos travel faster than the speed of light—for the joke to be funny.
It's only when you want or need someone to believe what you say or do what you suggest that more than just words are needed. If your words suggest that desire or that need, and you don't have a tight logical argument from premises that your readers already accept, there's nothing unfair about them asking, "who the hell are you?"
This is Internet anonymity in a microcosm: When Carolyn Elefant posts at My Shingle looking for crowdsourced advice for a struggling solo, her first, longest, and most vocal response is from someone anonymous, a dabbler in criminal defense (by which I mean he claims that criminal defense is "one of his practice areas"). This person is offering advice. But there's no logos to it; virtually every assertion he makes is baseless ("Hire an internet service to get you hits." Really? Why? What's the basis for that assertion?). There's also little pathos (except for the struggling solo's already-existing fear of failure) and, because he's anonymous and everything he alleges could be a lie, diddly-squat for ethos. So there's no reason for anyone to follow his advice, or even to take it seriously. That might change if he just revealed his credentials. Yet, in defending his prescription, he asks, "How would I be more persuasive if I was non-anonymous? A valid argument either stands or falls on its own merits."
The answer to the question should be obvious: his advice is not a logical argument that stands on its own merits. Some of his advice may be correct, but he doesn't demonstrate that it is through any sort of reasoning or evidence. So if he wants thoughtful people to heed him, he is going to need something more, and there's no reason for him to be shocked, alarmed, or offended when people suggest that.
The Internet may have contributed to the dumbing-down of America. It's possible that people are more credulous now than they were twenty years ago, more willing to believe things that we read just because someone typed them somewhere. But I doubt that the credulity extends to a struggling solo making decisions that will affect her and her family's future. She will look for advice from someone who can demonstrate that he knows what he's doing (which is why she emailed Carolyn).
Look: I've been solo for sixteen years, starting right out from law school. I make a great living doing work that I enjoy while having lots of time for the other things I love. I have a nice office downtown, and a nicer house nearby. When I offer practice-building advice to young lawyers (it doesn't include "hiring an internet service to get you hits," nor "spending half your gross on advertising," nor "getting into an area of the law just for the money"), they can see that I know what I'm talking about. I don't need to build a rigorous argument for not hiring Yodle. In the field of succeeding as a solo, I have ethos to burn.
Ethos is not all I have, though. I can demonstrate by giving examples why a lawyer concerned about his reputation should not hire Yodle or FindLaw (logos), and can frighten you with the consequences of outsourcing your marketing (pathos). Perhaps I could be as persuasive on the subject writing anonymously as using my name, but it would be more work.
Oddly, while the value of anonymous** commenters' writing is more dependent on support and logic than it would be if they had some skin in the game, they are less willing to put in that sort of work.
*Looking to see if anyone has tilled this particular field this before, I saw that John M. Regan, Jr. has written about anonymity and rhetoric on the internet, with a shallow gloss on Plato's views of rhetoric, and more on Aristotle.
Shorter Regan: the Internet is all about theoretical, intellectual analysis, in which rhetoric has no role; besides, even in rhetoric, ethos is of little importance.
My response: Theoretical, intellectual analysis is fun, but rhetoric is persuasion. Turn your back on rhetoric, and you might as well give up the practice of law and run away to Canada.
Ethos is just one part of rhetoric, but the vast majority of online commentary is lacking in pathos and short on logos as well. The witness on the witness stand is using ethos and pathos just as much as the lawyers are.
Neglect ethos, and you will lose. That was part of Regan's problem when he was trying, anonymously, to persuade lawyers to take concerted action. He might have done better had he realized that persuasion takes more than theoretical, analytical analysis. Could it have been part of his problem in the case that drove him to flee abroad?
**As opposed to pseudonymous. Many people have online personas that, while not necessarily easily traced to their meatspace personas, are no less real. There's a difference between Ken at Popehat, or TJIC, and "anonymous" or the guy using a burner pseudonym.