I don't use a pen name. Everything I say goes out under my real name. I figure some people won't buy my books because of my views - and others will look for them because of them. It should even out.
Other people use pen names. Sometimes a writer will use a pen name to "brand" something in a different genre. Men who write romance often use female names because, well, "men don't write romance" (Nicholas Sparks is making a pretty good career, but he's really the exception that proves the rule). Some women speculative fiction writers still use gender neutral names. Another reason might be that the writer's own name is hard to pronounce or spell.
Some, though, use pen names because their families wouldn't approve of what they write, or their employers. (Very, very few erotica writers use their real names for this reason). Which brings me to: Anonymity.
The strongest argument against anonymity is that people will be more honest if they have to apply their real name to what they say.
Thing is? That's also one of the strongest arguments for anonymity.
There are people online who would be fired if their employers knew their real political views, their real sexuality, etc - and in some states, yes, employers can get away with this. Or, of course, there might be something going on in a company that needs to be revealed, but the employee revealing it is afraid of retaliation. Whistleblower protection only goes so far - especially if the person has children or other dependents.
Then there are still countries where people can be arrested or even executed for their views.
Also, there are teenagers who are seeking support for and help with problems, who can't go to their parents for whatever reason. Boys who know their father would get out his belt if he knew they were gay. Girls who might be pregnant, and who might face being disowned for it (or worse, in some more extreme Muslim communities. Honor killings are still a thing on this planet).
There's two sides to it. Being anonymous might make somebody who's inclined to be a troll or a bully more likely to be a troll or a bully.
But there's also a huge swathe of people for whom being anonymous is the only way they can actually be honest.
It's easy to say people should be able to speak out under their real names - and in an ideal world, they would.
We don't live in an ideal world.