If Alizée actually wanted to be big in the US (I don't think she wants to) there's one big reason it will never happen: her singing in a language that's not English. Can anyone tell me of any artist that made it big in the US not singing in English? It can't be many.
Besides, I think you made a good point with your post. It would take a
lot of effort if she wants to succeed, and she already lives a good life in France, so why bother?
(BTW, I think you're giving her a bit too much credit for her English skills.
)