Precisely. You have pointed out that free speech is a right because of the utility of it, to the greater good.
Of course it feels good to express yourself, but that's not why we have it as a right.
Restricting rights to the greater good is no good. In fact, it's bad.
I just want the right to express myself, and I'm willing to cede that right to everyone else, regardless of what I think of the utility of it.