I recently did a cross-country move and did some pruning of my books. In thinking about what to keep, I realized that as far as practical considerations go, I could have just scanned the bar codes, made a list, and gotten electronic editions of anything if I ever needed to read it again. I instead kept most of them, but for entirely non-practical reasons.
I think people born today just aren't going to have the same emotional connection to physical books. For me, growing up in an age of information scarcity, they were a gateway to wonders. And even now, like the author, they're a reminder of where I've been, a map to the interior of my head. But I'd be wildly surprised if my teen relatives, many of whom are avid readers, ever built up libraries large enough to be cumbersome.
So when I kick off, I fully expect that my treasured books will be scattered to the winds. If I'm lucky a few will be taken as keepsakes. But as a library, I expect it will die with me.