It's not just about the immutability of it all but also about your reputation and if you have your real name and face linked to your account it could mean a lot more potentially.
I think, having your real name and face linked to your account definitely shows realness without compromising freedom, at least better than anonymity from a social aspect.
Yeah it's more the freedom of thought and opinion I was referring to, like say, you wanna criticise something but a friend of yours on here might remember you've done the same thing in the past. It doesn't make your criticism less true but you'll know they'll read it and think of you as a hypocrite or whatever if you're trying to help someone else so you rather not say anything.
Things like that, aside from things being immutable that may put some people in a more defensive stance about more casual/social interactions/discussions, this could be another barrier where some may choose not to be as open as they'd want about certain things. With anonymity that isn't as big of an issue.