I get this logic, and it would fit better with the rest of my personality if I treated books this way, but I don't. Instead I have maybe 100 books, 90% read, even after culling stuff I don't like about once per year. And my default is still to buy books. Some reasons for this are:
1. Books are pretty cheap. If you're looking for something more than 15 years old, you can probably find a cool-looking used paperback on eBay for $4-5 shipped. This isn't as cheap as "free at the library" but my book habit still sets me back 2. Some people (including me) like books as aesthetic objects. Maybe there is some element of "mmm, I am so smart" when I look at my bookcase, but it's also just a nice wooden case with a bunch of colorful objects in it. I like having it around.
3. It's fun to look at your old books and remember what it was like to read them. My books are physical objects that I actively thought about, held in my hands, and carried around for a week or whatever years ago, so it's a surprisingly effective way of conjuring up time and place.
4. Giving away books to friends is fun and makes it more likely they'll actually read the thing.
5. As a kid I loved big shelves with lots of books, they suggested so much possibility and I'm glad my parents had so many. If I ever have a kid I would enjoy providing them with a similar environment.
So buying books doesn't make much sense from a pure information acquisition standpoint, but there are some more idiosyncratic benefits.