Rehearsing probably helps for speeches, but I think other sorts of public speaking don't need it as much. Particularly, I am not very likely to deliver a speech; I am much more likely to give a talk or presentation on some subject. Given that I know the subject well, I find improvising the exact wording--not the content or structure--is best for me.

That said, giving a talk about something you know well to a group of people naturally interested in that subject is probably much easier than giving a speech (as long as you know what you're talking about, of course!).