As many above have pointed out, there is little reason to read the entire series "like a novel" from cover to cover, in addition to the fact that yeah, it would take a while to WORK through it like a textbook as opposed to read through it quickly to see what is there. And yeah, there are better books now in profusion on many of the topics covered, although AFAIK there is no book or book series that is as encyclopedic on the subjects he covers.
However, many people will find some of the sections very useful. I personally found "Seminumerical Algorithms" useful indeed when learning about random number generators and testing random number generators. It isn't the last word, and it certainly isn't the latest word as we move into a 64 bit world and beyond, but it is an excellent starting point. In other parts of the series there are other gems or nuggets well worth studying or reading, even if you move on to actual research papers or better books afterwards.
To sum up, it is a useful thing to own if you are doing a lot of very widely spread code development and need to acquire literacy quickly in subjects it covers, even if you are going to end up looking for an O'Reilly text on some of those subjects to get a more modern perspective. Those OR books are probably going to reference, rewrite, and augment Knuth.
Note well that I'm an Old Guy (tm) and actually did write a lot of code in Fortran once in the long ago before abandoning it for C and Unix and beyond. TAOCP was one of the ONLY really good encyclopedic references for people who were NOT CPS majors and who needed to learn about algorithms of one sort or another or some aspect of coding covered in one of the many CPS courses they never took. They (I) didn't need a course with the best textbook of the day -- we needed to get started. Once started, we knew how to learn and go beyond the start. 1.5 cubic feet of shelf space wasn't too high a price to be able to learn something about everything or anything to get started.