Let's say, like many people, you enjoy the occasional article from The Onion. You can very easily continue enjoying them without reading Animal Farm, Gulliver's Travels or the collected works of Aristophanes.
TAOCP, to me, is in a similar category - it's worth remembering Knuth essentially carved the field of study out himself. If you need a reference or textbook, there are by now better places to start. If you are interested in the field, you should definitely get a hold of TAOCP as well. But you can be a perfectly fine and educated programmer (let alone person) and never touch the thing.
I completely disagree that TAOCP is a "reference work" or that invariably there are "by now better places to start". If you care to learn about any of the topics in TAOCP, to the level of detail it contains, it is usually one of the best places to read. Knuth has taken the entire mass of published literature on the topic, passed it through his "interestingness" filter, and boiled it down to usually the best writing on the topic.
For example, suppose you want to learn about Binary Decision Diagrams. I have before me TAOCP Volume 4A, which has 57 pages of text, 22 pages of exercises, 58 pages of answers, and a wealth of references. (Section 7.1.4, you can see the draft Fascicle 1B online: http://www.cs.utsa.edu/~wagner/knuth/) There are simply no other books or papers where you can learn so much about BDDs and ZDDs this well or easily. The writing is crisp and clear, and is really intended to teach, not to be a reference to look up.
Of course, a lot of people have simply no need to learn about zero-suppressed binary decision diagrams, so they can just simply not read TAOCP. But that's a different claim from saying that it's a reference work or not a good read on its topics.
Fair enough. BTW I do agree with your original comment that started this thread, that GEB and TAOCP are nothing alike. I greatly enjoy the experience of reading both of them, but for very different reasons.
I agree that nobody needs to read TAOCP (or, really, even any equivalent textbook) to be a good programmer.
I disagree with how you've characterized it. I'm unlikely to ever read all of TAOCP and, yes, the reason for that is that doing so would feel a little bit like a commitment to read the whole OED from cover to cover.
But in fact TAOCP isn't really a reference book and it is pretty rewarding, in a straightforward, professional sense. I dip in and out of it sort of at random and I can think of several times when doing so has made me sharper, or when I directly took something from TAOCP and ended up applying it.
My takeaway from this is that TAOCP is a super weird book, one we can't really put our finger on to characterize.
It's written much better than any reference book has any business being written. It's also very much intended to be both a survey and a reference work, among other things. But at this point, we've shaved the yak to a smooth shine and are carefully splitting the yak-hairs one by one. GEB ain't no TAOCP.
I'll be frank, I think that Knuth's analyses have surprisingly fresh and useful approaches, particularly compared with the other algorithms texts I've read. The usual texts are better at compressed results and a "Straight path" through, but as ways of thinking, I find Knuth more useful to study.
I wouldn't recommend TAOCP to anyone not interested in algorithms, mind.
Oh, I'm an unrepentant TAOCP and Knuth fanboy. TAOCP is undoubtedly a Great Work™. I'm just bothered by the notion that someone would feel bad or inadequate for not having read it.
GEB, on the other hand is... I dunno, an ok monitor riser if you don't have anything else handy.
TAOCP, to me, is in a similar category - it's worth remembering Knuth essentially carved the field of study out himself. If you need a reference or textbook, there are by now better places to start. If you are interested in the field, you should definitely get a hold of TAOCP as well. But you can be a perfectly fine and educated programmer (let alone person) and never touch the thing.