Usually I reach for TAOCP with a reasonably clear idea of what specific problem I’m trying to solve and what class of algorithm I’ll try to find in there. So if you find yourself in this position at times, then might he worth the investment, otherwise I’d perhaps go for something like the Cormen instead, which can actually be pleasantly read cover to cover to get a better sense of the landscape, so to speak.
Personally I wouldn’t read TAOCP from cover to cover, the uncompromising rigor makes it quite the tough read.