Honestly, despite everyone's claims of how "beautiful" the books are, I think they are rather terribly formatted.
For example, the first volume consists of 2 "chapters". Each chapter spans about 250 pages on its own. So actually not a chapter, but a section, or maybe even a book in its own right. Then, each chapter is broken into sections and subsections that flow one into the next. There's a fundamental lack of whitespace and breathing room in a book that is supposedly "beautifully formatted".
At the very beginning of the book, there is a flowchart for how you're expected to read the book. It's not linear. It's not even close to linear, even within a specific topic. So why not just format the book in the suggested reading order?
I don't agree that Knuth is a great communicator. He's verbose when he could be succinct. He's taciturn when he should expound. He's prone to flowery language with humorous barbs in his introductions (and they can be quite funny, if you are clued in enough to what he's talking about already), but then spews dense mathematical notation when he gets into details.
So yeah, there's a lot of interesting information in the book, but it's a struggle to read it. Some people will say it's supposed to be a struggle, it's meant to make you work. Why? Programming is already hard on its own. Why make the act of reading about programming hard, too? I think, for the amount of effort being put into them, they could have been written more clearly. It makes the books feel like they are designed to mark an in-crowd of mathematicians who learned programming rather than to teach people computer science.