As an aside, I think Alice highlights for me the uniqueness of the Irene Adler/Moriarty character in Elementary. She had a tiny failure of perception when it came down to Joan and her own feelings for Sherlock, and paid dearly for that, but how much do I love that her plan was mostly about making a billion dollars, and Sherlock was mostly a tool? We desperately need more female characters like her — like Joan! — whose activities are self-directed, and not necessarily relational (e.g., out of revenge, love, etc).
In that sense, I think what I've seen so far of Alice (I just watched S2E01, and of course she wants to see Arecibo, I do wonder if she ever thought about SETI as a metaphor for her own existential situation) sells her short. We've seen her do the family thing, and being fascinated by what she must see as Luther's baby steps towards the self-awareness she knows he's capable of (Alice Morgan: a more persuasive Joker)(also: Alice Morgan wants a friend, so run), but what else has she been up to? What else is she doing? She's this world's Moriarty; it doesn't seem as if she wants money or power, and I can definitely believe that intellectual stimulation is her stock in trade, which is why she does astrophysics and plays with/around Luther, but I don't buy for a second that somebody with her obvious skills, experience, and energy has only done what we've seen her do.