Their justification was that TAOCP had never been checked out. Which is funny because the year prior when I tried to check out a volume, they told me it was a reference book and could not be checked out.
I'm still completely confused about how that decisions was actually made, and why the books weren't given away or sold.
TACOP is extremely dense and put me to sleep every time I tried to read it. I recently donated my copy of 0-4 to my work library, where nobody was interested in reading it.
The fact that we both have opposite views of your example books shows that this is a difficult process for librarians.
That said, I never worked through the remaining chapters of the series, and likely never will. It's a reference book. Read the sections as they pertain to you. For instance, TAOCP was my introduction to sorting networks. This led to direct, measurable, improvements in a few embedded programs (where consistent, deterministic behavior, and optimal behavior, were strongly desired).
I mean, few people ever read a dictionary. I still have one on my desk at home and at the office. This isn't substantially different (though I do recommend skimming it so you are aware of what resources it contains for later reference).