Because if we let people be anonymous, then more people will feel comfortable writing insightful things for us to read. I'd rather have a wider selection of content than know everyone's real name. Knowing who writers are "in real life" is useless and uninteresting most of the time.
In any case, blogging anonymously is certainly technologically possible. And it's neither illegal nor immoral. So I think that makes it a right, no?
Anonimity is certainly not a right but sometimes is the only protection for other rights. And we must acknowledge the consequences of technology, unintended or not. For example, nobody expects privacy in public spaces but I think everybody agrees camera surveillance can be abused. Sometimes quantity is a quality of its own.
It's not a legal right if that's what you're getting at. Otherwise, do you also not understand why basically all platforms have pretty assertive (if questionably enforced) anti-doxxing rules?
Where’d you get that idea? You not only have a right to privacy in your own bathroom, the courts have declared a reasonable expectation of privacy inside public bathroom stalls, and/or behind privacy partitions. CNN publishing nude photos of anyone going to the bathroom would generally be completely illegal.
In any case, blogging anonymously is certainly technologically possible. And it's neither illegal nor immoral. So I think that makes it a right, no?