I tend to avoid anything popular history like the plague unless recommended here or by another scholar, but Amy Chua's Day of Empire: How Hyperpower's Rise to Global Dominance and Why they Fall is a required text for one of my classes. I read her introduction, and am skeptical of her thesis. I think she puts too much of an emphasis on the importance of toleration within Classical Rome, and kept mentally screaming Spain when she stated an intolerant civilization cannot be a world dominant power; apparently she addresses Spain in a later chapter but I have yet to get there.
I was wondering what the professionals generally think of her work. Specifically the ideas, and the thesis rather than the book itself (I know the book is going to over-generalize).
My understanding is that the thesis of that book is not about history, rather that she uses historical anecdotes to support her thesis, so I'm not sure that /r/AskHistorians/ is the best place to ask this question. Unless you have specific history-related content from that book you want to ask about. While I don't have access to that book, I did suffer through "World on Fire" and in my opinion she tends to fall into the trap of historical determinism, in addition to glossing over counter-examples as you mentioned.
Maybe you can try /r/Ask_Politics/ or some other sub?
I hope that class that assigns that book isn't a history class :D.
Edit: a related question you may be interested in.