Any 400 page book that tries to summarize the development of human knowledge over time must necessarily omit some ideas. The problem being, which ones do you leave out?
Van Doren sticks mostly to Western Philosophy and its maturation into Mathematics, Physics/Chemistry/Biology, History/Sociology/Psychology/Economics, and Political Economy. While this appears to be correct, Van Doren tends to assign too much power to ideas in history (Rome's logical armies beat out Greek navel-gazing forces; Europe was bored, so we went into WW1, etc.). Even worse, he advances novel claims (Christians extended the Dark Ages by being too pious and concerned with their souls instead of making life easier and longer).
I would like to have seen a more constructivist approach taken. Ideas need people with enough time to produce them, and then they need a way to disseminate. Wars, famine, and disease all get in the way of idea propagation. Chances are, the first ideas that lasted were ones that helped people get along together, make enough food, keep that food for themselves, and helped them have more children and stay alive longer.
From that initial idea stage, we can see what ideas develop and how they fare amid the reality of wars, food production, and disease. That interplay would be quite interesting. But I've not heard of such a book, have you?