Isn't this related to the book shelves themselves? If you look at the book shelves in the Willow Creek library they are not the same ones you can buy in build mode. What I did was I put a few of the shelves from the Willow Creek library and saved them in a room. I use the book shelves from this room in all libraries that do not have them.
As @danacnbrett said, a work-around is to save a bookcase from Willow Creek Archives as a separate room in your gallery then add that room to every library lot in the game. Just adding the bookcase room to the library lot seems to update all shelves to contain skill books, in the same way that adding a toddler bookcase to a lot adds the toddler books to every bookcase. You don't even need to keep the Willow Creek bookcase on the lot. Once the shelves have updated, you can take it away and the skill books will remain.
I've tested this work-around in modded and unmodded files, and several different library lots, and it's worked every time.
I apologize for not being able to come back until now. Anyway, I ended up replacing the libraries with originals from a new fresh save. I just saved them to my library and then placed them in the other save and now everything works. I need to add though that I also got rid of all lots and Sims I'd downloaded from the Gallery. You're right that the bookshelves in the Willow Creek Library were different in the Lil Simsie lot I'd downloaded, they weren't the original ones.
All I can surmise is either that's why the shelves in all libraries didn't have skill books or perhaps the Librarian Sim I had downloaded or one of the other lots. None of them were supposed to have CC in them, CC doesn't transfer from the Gallery from what I've heard, so I doubt it was a CC conflict. I don't have CC/Mods in my game and I never have. Though the problem is fixed for me now, it's still a mystery though because I had tried to replace those bookshelves with in-game ones that looked exactly like the ones in the original Willow Creek. Plus, the Windenberg Library was the original one, it hadn't been replaced and wasn't working.
I suspect the Librarian I downloaded. But I'm not sure... *shrugs*
