
The first revision of this third volume is a survey of classical computer techniques for sorting and searching. It extends the treatment of data structures in Volume 1 to consider both large and small databases and internal and external memories.
That's probably true, in the sense that it deals largely with the kind of functionality modern programmer should be calling from a library, not implementing by hand. But I think it's hugely enriching to read these books. I read 1-3 back in the 70s, and was particularly inspired by Sorting and Searching, and especially the chapter on random numbers. RNGs have intrigued me ever since.
I find Knuth's writing style very pleasant. He's funny. So is it worth the time and effort? Not if "worth it" means "makes you a better Javascript programmer". But it's worth it in the sense that reading books about the history and geography of a country is "worth it" before visiting; your appreciation of the place is deepened, possibly transformatively. It could even be that you would never have visited had you not read those books.
I found TAOCP easy to read, much more so than most textbooks. I don't think I tackled many of the exercises; certainly none of the challenging ones. So for me, the "effort" aspect of "is it worth the time and effort" was quite low, so the ROI was quite high. If you find the books hard to read, then don't bother (and perhaps you aren't really interested in low-level algorithms).
I read some of Vol 2, Seminumerical Algorithms, to hone my instincts on how random numbers work in practice. I have referred to it on occasion when people say things like, "if we seed the random number generator, take the random number, then feed that into the seed, the result would be more random."
I read most of Vol 3, Sorting and Searching, when applying for jobs. It was more interesting than leetcode grinding. I don't know if it was more useful, but it was better for my sanity.
I barely scraped through with a C for Engineering Math (Differential Equations).
For me, the teacher made the difference in math.
For CS, the most influential books for me were Knuth, Sorting and Searching (although I actually bought all three books in the series, unlike most others I knew), as well as the original Kernighan & Ritchie book on the C programming language (before ANSI C was published).
For moderately impractical, look at tape sorting in Sorting and Searching.
It's a great work (I'd be lying if I'd said I'd poured into the entirety of it extensively, but I've spent weeks on certain portions, like the MMIX fascicle and Sorting and Searching), but PAIP has a significantly better claim at "kickstarting" the "read code instead of write it" trend, because in TAOCP the code doesn't take center stage, and it was never the point for it to (hence the creation of MIX & MMIX).
For not entirely clear reasons (maybe multiplier selection?), only Knuth's modulo prime suggestion "propagated" well in the 70s and 80s. This suggestion reception bias also aged poorly over ensuing decades with the CPU cost of modulo vs. multiply evolving from a 2x performance delta to more like 10x.