Frankly, I don't think I want to know what a bunch of non-anonymous people think of me either. Though please do mention it if I sat in gum.
I also thought that anonymous con-crit meme a few months ago was weird, though not in the same way. I think crit is most useful when you can put it into context. Like if a friend tells you that a movie sucks, you can put that in the context of what other movies she's enjoyed or disliked and how her taste aligns with yours and whether she's smart or dumb. But if a stranger says a movie sucks, you have no basis to evaluate his opinion.
In fandom, even if you don't know someone personally, you can see what they like to read and what they write (if they do) and all those other little things that help us form an opinion of someone (like maybe looking up what everybody said about them in the brutal honesty meme). But if they're anonymous, how do you know how seriously to take them?
In other news, I like cheese.