Most books don't age well, you're correct. Which is why you should read old books. Old books that are still around today are actually the few that were good enough to keep around. The crappy books from back then have long since aged out and been forgotten.
Meanwhile the "bleeding edge" is still so new, that the crap hasn't aged out of it yet, so your good-to-crap ratio is going to be lower. And while I'm on the subject of crap, don't read too much self-help - not that it's necessarily crap, but being a motivational type thing, it tends to be, essentially, a sales pitch - either for the ideas in the book itself, or possibly for more cynical things such as ancillary product$ or other book$, or for the author's cult of personality. That sort of thing will tend to be, as you said, filled with disconnected fluff/anecdotes/stories etc.
Though at the same time I had to laugh that you complained that "... books ... were mostly filled with ... stories." Yep they sure are! Done right, a story is sometimes the best way to tell something. Problems can be solved obliquely don'tcha know. You might learn more about "How to Win Friends and Influence People" (to pick a classic self-help title) by reading something like Dostoyevsky (though I wouldn't recommend that as a first try).
Get you some fiction. A book that captures something of the universal essence of being human, that's a book that can transcend time, and that's why, again, somebody and a bunch of other somebodies decided to keep reprinting or republishing it. Find a book or an author you believe in, that you consider worth it. Because that was your question. It's partly a self-fulfilling answer. Are books worth it? Read some books and find out.
Any time you skim something, you are putting yourself above the author, making yourself their editor essentially, deciding which parts of what they wrote, needed to actually be written and which parts can be skipped. You're probably not even reading this now, huh fucker? Ha, got you. Seriously though, find an author you can trust, and then surrender to them and their book more. Instead of thinking you know best what can be skipped, actually assume the author knows what they're doing, and wrote all those words on purpose. That won't work if you don't trust them, and it won't work if the author is no good (i.e. can't be trusted).
I bet this approach will also make you, to a surprising degree, remember stuff, whereas before, you (maybe correctly) surmised that nothing in the book was particularly important. You probably had yourself a crap writer right there, that's what that was.