Nice approach. I personally can't force myself to get rid of books that I've read, which is not very rational, because I very rarely reread books. But other stuff I try to get rid of, or not buy at all.
It doesn't make sense to stockpile books on the chance that your children might one day want to read them when a used copy is generally a click away. (Not to mention that you may prefer to re-buy them in digital form.) Every square inch of space in your home has a carrying cost (I used to calculate $4 per net square foot per month in New York).
Having one less book shelf is effectively saving enough per year that you could probably pay for buying back all the books you'd ever re-read on that shelf. And if you ever move, the cost and annoyance of keeping books just skyrockets.
I have a lot of books I love, but 90% of books are essentially disposable vehicles for information of transient value.
My kids can't browse books that are no longer on my shelves. I encourage them to pick up a random book and explore it. It's kind of like having a hard copy of the web without distractions, and I can see them making their own connections from the words, rather than following links prepared by someone else.
I wouldn't under-estimate the value of this as an experience for kids. I discovered a copy of "Saturday Night and Sunday Morning" by Alan Sillitoe in a pile of old books my parent had. It was like discovering a small nugget of gold.
My parents were a book household too. But back then, there was no Internet, no e-books. The only place to wander onto a book was your shelf or the local bookstore. Times change.
I get rid of them. My forcing function is that I won't buy any more shelves - I have two bookcases with about 4 shelves each, shared with my girlfriend, and if I want to keep a book I have to get rid of one. It's still probably 300 lbs of books but it keeps it bounded. (And a lot of those are hers, because she went to law school and still has many of her law books. Most of mine are design or cooking, since the color plates don't really have electronic equivalents yet and some are signed.)
Also, for text-only, transient stuff like business books and history books (that I'm unlikely to read twice), I buy a lot of Kindle stuff now.
Extremely interested in this idea - I've gotten to the point of pricing out FedEx-Kinko's to cut the bindings off ($1/ book actually) and then scanning them dual-sided into Evernote with searchable text (if you're a Pro member it scans inside PDFs).
Still can get past the cognitive dissonance of letting my bookshelf go.
I do re-read books, but only some. I've set myself a target of reducing the library in size by a factor of two over the next year, simply through space constraints.
The decision making is forcing valuable reflections!
I now have children who want to read them.