Question: Is there a symbolic reason why Alice and Anna are both American? Or was it just a coincidence with the choice of actresses?
Answer: This is not an official answer, but my interpretation is that them both being American makes them interchangeable, in a way. Whether Dan or Larry is involved with Alice or Anna, both men have issues that cannot be totally helped by a relationship with either woman. Although, Larry and Anna only spent a night together.
Answer: It might be simple coincidence. According to some online searches, the role of Anna was almost played by Cate Blanchett, then Nicole Kidman. Both of them are Australian, so I don't think it was intentional for both women to be American.
Answer: I think it mostly has to do with the casting of Natalie Portman and Julia Roberts. In the original play, there's no mention of Alice or Anna being American.