Funnily enough, I commented about Anya's speech to my husband the other week when we were watching 'The Wish' again, and I do agree with Lily, I think that at the time they probably hadn't intended for her to become a regular member of the cast, so they hadn't even thought of how she would speak etc.
Obviously once they'd determined that Anya would become a regular face they had to give her character more depth and show the viewers how out of touch with her humanity she was - hence her wearing her emotions on her sleeve so to speak, her lack of understanding of human traditions/values etc, and also the way in which she actually talks too.
In my opinion this was done to reiterate the fact that she was having to learn, almost like a child, how to behave in society and to accept the fact that she was now human again, something she hadn't been for such a long time. 🙂 It gave her character more credibility to have her behave like that, instead of just having her behave like everyone else.