I see these challenges as a great way for excellent experienced developers to weed out incompetent companies. I'm a kick-ass get-things-done full-stack web engineer. I've never had to deal with one of these sorts of problems in my day to day work; and if I did, I'd just find an existing, tested, stable library that already handled them. A company that needs someone to solve these sorts of problems doesn't want me on…
I was going to agree with you, 98% of my career has been "google for a library, then use or tweak". It's RARE we ever actually do anything "new". However there ARE companies that do, and every once in a while YOU may have to do something new. In those cases it's good to make sure you have a foundation to build on. I have 4 books in the "The art of computer programming" series on my desk. They've been more or less dec…
The background knowledge to understand what you're looking for and looking at is really important in these cases. You mention having and having read TAOCP, that already puts you ahead of >99.99% of the people doing programming out there - 95% of whom couldn't tell you who Knuth is, what he's written, or what Drofnats refers to.