> my impression is that they were chosen by a generalist mathematician rather a specialist in each of the areas -- in optimization for instance, some of the topics would not be developed or weighted in quite in this fashion in a state-of-the-art course.
Yes. Compared with this book, the one semester course "Foundations of Optimization" I took was better balanced and usually deeper.
> I want to say this could be a good handbook
I see it as best as a handbook. So, e.g., if hear about some topic X, want to know more, and find a treatment in this book, then give the book a shot but don't take the book too seriously as the balanced view of an expert.
> advise readers to consult texts written by experts in each subfield to get a sense of what topics are important and what are not.
Yes. And not just for "a sense" but for the actual content. E.g., I would go to some of the books in my professional library for the numerical analysis, linear programming, non-linear programming, regression analysis, Hilbert space, exterior algebra, abstract algebra, Lagrangian techniques, etc. And in the table of contents I didn't see anything on network flows which, considering what else is in that book, is a curious omission.
But, again, in summary, if want to know about topic X that is in the book, then likely give the book a shot, at least for a few minutes.
One more point: For students who want careers in academic research, one reason, likely the most important reason, to study such advanced and specialized topics is as an introduction to some promising streams of research. Well, I'd try to avoid using this book much for that goal and, instead, look for better material from better sources.