Not only that, but it also serves a very valuable purpose: It allows people to have "unpopular" opinions, only to realize that they may be more popular than they thought.
I don't know if anyone here ever played the RPG "Paranoia". It stopped being fun when it became too close to home for comfort. It was a world under total surveillance where mutants and members of secret societies were hunted. The fun part now was that EVERYONE was a mutant and EVERYONE was member of some secret society. And everyone thought they're a tiny minority and everyone else is out there to hunt them down, because that was the generally accepted dogma and everyone was happy when someone else was being hunted because it means that, at least for now, they're not on the hunt list.
Sounds familiar? It should.
What anonymity allows in the context is that you can find out that you're not alone. That you're not the "odd man out" if you don't think the generally accepted dogma and creed is the all encompassing truth but that basically everyone thinks like that. Only the ones that hold power and media do not.
Of course, this is a threat to those that have power and media outlets in their hands. If you can convince everyone that they are alone in their "resistance" against the official opinion, they will conform. If you can threaten them with indirect or direct repercussions if they disagree, they will fall in line, even if they could in theory voice their opinion. Just lock up everyone who dares to speak out and people will think that that guy and they are the only 2 in the world who thought like that.
If people can voice their concern anonymously, they will soon find out that they're not alone. Not by a long shot. Actually, they will find out that the official opinion is backed by nobody but a tiny minority.